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href="/cbse/cbse-extra-questions/">CBSE Extra Questions</a><ul> <li><a href="/cbse/extra-questions-for-class-8-maths/">CBSE Class 8 Maths Extra Questions</a></li><li><a href="/cbse/extra-questions-for-class-8-science/">CBSE Class 8 Science Extra Questions</a></li><li><a href="/cbse/extra-questions-for-class-9-maths/">CBSE Class 9 Maths Extra Questions</a></li><li><a href="/cbse/extra-questions-for-class-9-science/">CBSE Class 9 Science Extra Questions</a></li><li><a href="/cbse/extra-questions-for-class-10-maths/">CBSE Class 10 Maths Extra Questions</a></li><li><a href="/cbse/extra-questions-for-class-10-science/">CBSE Class 10 Science Extra Questions</a></li></ul></li><li class="sub"><a href="/cbse/cbse-class/">CBSE Class</a><ul> <li><a href="/cbse/class-3/">Class 3</a></li><li><a href="/cbse/class-4/">Class 4</a></li><li><a href="/cbse/class-5/">Class 5</a></li><li><a href="/cbse/class-6/">Class 6</a></li><li><a href="/cbse/class-7/">Class 7</a></li><li><a href="/cbse/class-8/">Class 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itemtype="https://schema.org/BreadcrumbList"><li itemprop="itemListElement" itemscope="itemscope" itemtype="https://schema.org/ListItem"><a itemtype="https://schema.org/Thing" itemprop="item" href="/maths/"><span itemprop="name">Maths</span></a><meta itemprop="position" content="1"/></li><li itemprop="itemListElement" itemscope="itemscope" itemtype="https://schema.org/ListItem"><a itemtype="https://schema.org/Thing" itemprop="item" href="/maths/articles/"><span itemprop="name">Math Article</span></a><meta itemprop="position" content="2"/></li><li itemprop="itemListElement" itemscope="itemscope" itemtype="https://schema.org/ListItem"><a style="color:black;text-decoration:none;cursor:auto" itemtype="https://schema.org/Thing" itemprop="item" href="/maths/geometry/" onclick="event.preventDefault()"><span itemprop="name">Geometry</span></a><meta itemprop="position" content="3"/></li></ol> </div> <div class="h1-banner-title"><h1>Geometry</h1></div>  <div class="widget top-banner-widget"> <a class="book-free-class" style="cursor: pointer;" target="_blank"> <picture> <source srcset="https://cdn1.byjus.com/wp-content/uploads/2023/06/Dark-BG-desktop-top.webp" media="(min-width: 768px)"> <img class="img-responsive aligncenter" src="https://cdn1.byjus.com/wp-content/uploads/2023/06/Dark-BG-mobile-top.webp" alt="Class Registration Banner" width="768" height="128"/> </picture> </a> </div>  <article id="post-116764" class="post-116764 post type-post status-publish format-standard hentry category-maths-article"> <p><span style="font-weight: 400;"><strong>Geometry</strong> is the branch of mathematics that deals with shapes, angles, dimensions and sizes of a variety of things we see in everyday life. Geometry is derived from Ancient Greek words – ‘Geo’ means ‘Earth’ and ‘metron’ means ‘measurement’. In Euclidean geometry, there are two-dimensional shapes and </span><a href="https://byjus.com/maths/three-dimensional-shapes/"><span style="font-weight: 400;">three-dimensional shapes</span></a><span style="font-weight: 400;">. </span></p> <p><span style="font-weight: 400;">In a plane geometry, 2d shapes such as triangles, squares, rectangles, circles are also called flat shapes. In solid geometry, 3d shapes such as a cube, cuboid, cone, etc. are also called solids. The basic geometry is based on points, lines and planes explained in </span><a href="https://byjus.com/maths/coordinate-geometry/"><span style="font-weight: 400;">coordinate geometry</span></a><span style="font-weight: 400;">. </span></p> <p><span style="font-weight: 400;">The different types of shapes in geometry help us to understand the shapes day to day life. With the help of geometric concepts, we can calculate the area, perimeter and volume of shapes. </span></p> <table> <tbody> <tr> <td><strong>Table of Contents:</strong></p> <ul> <li><a href="#Definition">Definition</a></li> <li><a href="#branches">Branches</a></li> <li><a href="#formulas">Formulas</a></li> <li><a href="#plane-geometry">Plane Geometry</a> <ul> <li><a href="#points">Points</a></li> <li><a href="#lines">Lines</a></li> <li><a href="#angle">Angle</a></li> <li><a href="#polygon">Polygon</a></li> <li><a href="#circle">Circle</a></li> </ul> </li> <li><a href="#solid-geometry">Solid Geometry</a> <ul> <li><a href="#edges">Edges</a></li> <li><a href="#faces">Faces</a></li> <li><a href="#vertices">Vertices</a></li> </ul> </li> </ul> </td> </tr> </tbody> </table> <p><a id="Definition" name="Definition"></a></p> <h2>Geometry Definition</h2> <p><span style="font-weight: 400;">Geometry is the study of different types of shapes, figures and sizes in Maths or in real life. In geometry, we learn about different angles, transformations and similarities in the figures. </span></p> <p><span style="font-weight: 400;">The basics of geometry depend on majorly point, line, angles and plane. All the geometrical shapes are based on these basic geometrical concepts.</span></p> <p><img class="aligncenter wp-image-13400 size-full" title="Geometry" src="https://cdn1.byjus.com/wp-content/uploads/2018/11/maths/2016/06/13102008/geo.png" alt="Geometry" width="800" height="400" /><br /> <a id="branches" name="Branches"></a></p> <h2>Branches of Geometry</h2> <p><span style="font-weight: 400;">The branches of geometry are categorized as:</span></p> <ul> <li>Algebraic geometry</li> <li>Discrete geometry</li> <li>Differential geometry</li> <li>Euclidean geometry</li> <li>Convex geometry</li> <li>Topology</li> </ul> <h3>Algebraic Geometry</h3> <p>It is a branch of geometry studying zeros of the multivariate polynomial. It includes linear and polynomial algebraic equations that are used for solving the sets of zeros. The application of this type comprises Cryptography, string theory, etc.</p> <h3>Discrete Geometry</h3> <p>It is concerned with the relative position of simple geometric objects, such as points, lines, triangles, circles etc.</p> <h3>Differential Geometry</h3> <p>It uses techniques of algebra and calculus for problem-solving. The various problems include general relativity in physics etc.</p> <h3>Euclidean Geometry</h3> <p>The study of plane and solid figures based on axioms and theorems including points, lines, planes, angles, congruence, similarity, solid figures. It has a wide range of applications in Computer Science, Modern Mathematics problem solving, Crystallography etc.</p> <h3>Convex Geometry</h3> <p>It includes convex shapes in Euclidean space using techniques of real analysis. It has application in optimization and functional analysis in number theory.</p> <h3>Topology</h3> <p>It is concerned with the properties of space under continuous mapping. Its application includes consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces.<br /> <strong>Also, check:</strong> <a href="https://byjus.com/maths/analytic-geometry/">Analytic geometry</a><br /> <a id="formulas" name="Formulas"></a></p> <h2>Geometry Formulas</h2> <p>To calculate the area, perimeter, volume and different measures using length, breadth and height of different geometrical figures, geometry formulas are important. By using the formulas, we can calculate the measures easily. There are loads of formulas to learn in Geometry. Here, you are provided with all the important geometry formulas in the PDF. Download the below-given PDF to learn and solve all the problems related to geometry.</p> <p style="font-size: 16px;"><b>Geometry Formulas:-</b><a href="https://cdn1.byjus.com/wp-content/uploads/2018/01/Geometry-Formulas.pdf"><span style="background-color: #2b3f84; border: none; color: white; padding: 10px 23px; text-align: center; text-decoration: none; display: inline-block; font-size: 14px; margin: 4px 2px; cursor: pointer;">Download PDF Here</span></a></p> <p><a id="plane-geometry" name="Plane-Geometry"></a></p> <h2>Plane Geometry (Two-dimensional Geometry)</h2> <p><strong>Plane Geometry </strong>deals with flat shapes which can be drawn on a piece of paper. These include lines, circles & triangles of two dimensions. Plane geometry is also known as two-dimensional geometry.</p> <p>All the two-dimensional figures have only two measures such as length and breadth. It does not deal with the depth of the shapes. Some examples of plane figures are square, triangle, rectangle, circle, and so on.</p> <p>The important terminologies in plane geometry are:</p> <ul> <li>Point</li> <li>Line</li> <li>Angles</li> </ul> <p><a id="points" name="Points"></a></p> <h3>Point</h3> <p>A point is a precise location or place on a plane. A dot usually represents them. It is important to understand that a point is not a thing, but a place. Also, note that a point has no dimension; preferably, it has the only position.<br /> <a id="lines" name="Lines"></a></p> <h3>Line</h3> <p>The line is straight (no curves), having no thickness and extends in both directions without end (infinitely). It is important to note that it is the combination of infinite points together to form a line. In geometry, we have a <a href="https://byjus.com/maths/horizontal-line/">horizontal line</a> and vertical line which are x-axis and y-axis respectively.</p> <p><img loading="lazy" class="aligncenter wp-image-13402" title="last_thumb13779896841" src="https://cdn1.byjus.com/wp-content/uploads/2018/11/maths/2016/06/13102421/last_thumb13779896841.jpg" alt="Lines in Geometry" width="448" height="194" /></p> <ul> <li style="list-style-type: none;"> <ul> <li style="list-style-type: none;"> <ul> <li>Line Segment – If a line has a starting and an endpoint then it is called a Line Segment.</li> <li>Ray – If a line has a starting point and has no endpoint is called Ray.</li> </ul> </li> </ul> </li> </ul> <p>Eg. Sun Rays<br /> <a id="angle" name="Angle"></a></p> <h2>Angles in Geometry</h2> <p>In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.</p> <h3>Types of Angle</h3> <p><strong>Acute Angle</strong> – An Acute angle (or Sharp angle) is an angle smaller than a right angle ie. it can range between 0 – 90 degrees.</p> <p><strong>Obtuse Angle</strong> – An Obtuse angle is more than 90 degrees but is less than 180 degrees.</p> <p><strong>Right Angle</strong> – An angle of 90 degrees.</p> <p><strong>Straight Angle</strong> – An angle of 180 degrees is a straight angle, i.e. the angle formed by a straight line</p> <p><img loading="lazy" class="aligncenter wp-image-13403" title="geometry" src="https://cdn1.byjus.com/wp-content/uploads/2018/11/maths/2016/06/13102516/geometry.jpg" alt="Angles in geometry" width="604" height="337" /><br /> <a id="polygon" name="Polygon"></a></p> <h2><span style="font-size: 16px;">Polygons in Geometry</span></h2> <p>A plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.</p> <p>The name ‘poly’ refers to multiple. An n-gon is a polygon with n sides; for example, a triangle is a 3-gon polygon.</p> <p>General Formula for Sum of internal Angles of a polygon –</p> <p><span class="latex-for-amp"><div class="mathjax-scroll">$\begin{array}{l}\text{Sum of internal Angles of a polygon = }(n-2)\times 180\end{array} $</div></span></p> <h3>Types of Polygon</h3> <p><span style="font-weight: 400;">The types of polygons are: </span></p> <ul> <li style="font-weight: 400;"><span style="font-weight: 400;">Triangles</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">Quadrilaterals</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">Pentagon</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">Hexagon</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">Heptagon</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">Octagon</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">Nonagon</span></li> <li style="font-weight: 400;"><span style="font-weight: 400;">Decagon</span></li> </ul> <table class="table table-bordered"> <tbody> <tr> <td><strong>Polygon type</strong></td> <td><strong>Definition & Property</strong></td> <td><strong>Types</strong></td> </tr> <tr> <td>(i) Triangle –</td> <td>A 3-sided polygon whose sum of internal angles always sums to 180 degrees.</td> <td> <ul> <li>Equilateral Triangle – Has 3 equal sides and angles.</li> <li>Isosceles triangle – Has 2 equal sides and angles.</li> <li>Scalene triangle – Has all the 3 unequal sides and angles.</li> </ul> </td> </tr> <tr> <td>(ii) Quadrilateral</td> <td>A 4-sided polygon with four edges and four vertices.</p> <p>Sum of internal angles is 360 degrees</td> <td> <ul> <li>Square – Has 4 equal sides and vertices which are at right angles.</li> <li>Rectangle – Has equal opposite sides and all angles are at right angles.</li> <li>Parallelogram – has two pairs of parallel sides. The opposite sides & opposite angles are equal in measure.</li> </ul> <ul> <li>Rhombus – Has all the four sides to be of equal length. However, they do not have its internal angle to be 90 degrees</li> <li>Trapezium – Has one pair of opposite sides to be parallel.</li> </ul> </td> </tr> <tr> <td>(iii) Pentagon</td> <td>A plane figure with five straight sides and five angles</td> <td>–</td> </tr> <tr> <td>(iv) Hexagon</td> <td>A plane figure with six straight sides and six angles</td> <td>–</td> </tr> <tr> <td>(v) Heptagon</td> <td>A plane figure with seven sides and seven angles</td> <td>–</td> </tr> <tr> <td>(vi) Octagon</td> <td>A plane figure with eight straight sides and eight angles.</td> <td>–</td> </tr> <tr> <td>(vii) Nonagon</td> <td>A plane figure with nine straight sides and nine angles.</td> <td>–</td> </tr> <tr> <td>(viii) Decagon</td> <td>A plane figure with ten straight sides and ten angles.</td> <td>–</td> </tr> </tbody> </table> <p><span style="font-weight: 400;">In the below figure, we can see the different types of polygons.</span></p> <p><img loading="lazy" class="aligncenter wp-image-13404 size-full" title="Types of Polygon" src="https://cdn1.byjus.com/wp-content/uploads/2018/11/maths/2016/06/13102733/geometry-21.png" alt="Polygons in geometry" width="800" height="400" /></p> <p><a id="circle" name="Circle"></a></p> <h2>Circle in Geometry</h2> <p>A Circle is a simple closed shape. From a certain point called the centre, all points of a circle are of same consistent distance, i.e. the curve traced out by a point that moves so that its distance from the centre is constant.</p> <h2><img loading="lazy" class="alignnone wp-image-13405 size-full" title="Circles" src="https://cdn1.byjus.com/wp-content/uploads/2018/11/maths/2016/06/13103043/Circles.jpg" alt="Circles in geometry" width="800" height="400" />Similarity and Congruency in Geometry</h2> <p><strong>Similarity</strong> – Two figures are said to be similar if they have the same shape or have an equal angle but do not have the same size.</p> <p><strong>Congruence</strong> – Two figures are said to be Congruent if they have the same shape and size. Thus, they are totally equal.<br /> <a id="solid-geometry" name="Solid Geometry"></a></p> <h2>Solid Geometry (Three-dimensional geometry)</h2> <p><strong>Solid Geometry</strong> deals with 3-dimensional objects like cubes, prisms, cylinders & spheres. It deals with three dimensions of the figure such as length, breadth and height. But some solid solids do not have faces (e.g. sphere).</p> <p>Solid geometry is the study of three dimensions in Euclidean space. The objects which are around us are three-dimensional. All the three-dimensional shapes are obtained from the rotation operation of 2D shapes. The important attributes of 3D shapes are:</p> <ul> <li>Faces</li> <li>Edges</li> <li>Vertices</li> </ul> <p>Go through these terms in detail for different geometric shapes here.<br /> <a id="edges" name="Edges"></a></p> <h3>Edges</h3> <p>An edge is defined as the line segment on the boundary that joins one vertex to the other vertex. It means that it joins one corner point to the other. It forms the skeleton of 3D shapes. In other words, it can be defined as the faces, that meet in the straight line is called edge. Following are the list of edges for the different solid shapes:</p> <table class="table-bordered"> <tbody> <tr> <td> <p style="text-align: center;"><strong>Solid Shapes</strong></p> </td> <td> <p style="text-align: center;"><strong>No. of. Edges</strong></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Triangular Prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">9</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Cube</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">12</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Rectangular prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">12</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Pentagonal Prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">15</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Hexagonal Prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">18</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Triangular Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">6</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Square Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">8</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Pentagonal Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">10</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Hexagonal Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">12</span></p> </td> </tr> </tbody> </table> <p><a id="faces" name="Faces"></a></p> <h3>Faces</h3> <p>We know that all the geometric shapes are made up of flat surface called faces. It is a flat surface enclosed by the edges. For any three-dimensional shapes, the face should be a two-dimensional figure. The list of the number of faces for different solid shapes are given below:</p> <table class="table-bordered"> <tbody> <tr> <td> <p style="text-align: center;"><strong>Solid Shapes</strong></p> </td> <td> <p style="text-align: center;"><strong>No. of. Faces</strong></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Triangular Prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">5</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Cube</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">6</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Rectangular prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">6</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Pentagonal Prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">7</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Hexagonal Prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">8</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Triangular Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">4</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Square Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">5</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Pentagonal Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">6</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Hexagonal Pyramid</span></p> </td> <td style="text-align: center;"><span style="font-weight: 400;">7</span></td> </tr> </tbody> </table> <p><a id="vertices" name="Vertices"></a></p> <h3 style="text-align: left;">Vertices</h3> <p>A vertex is defined as the point where the edges of the solid figure meet at each other. In other words, it can be said that, the point where the adjacent sides of the polygon meet. The vertex is the corners where the edges meet. The number of vertices for different solid shapes in geometry is as follows:</p> <table class="table-bordered"> <tbody> <tr> <td> <p style="text-align: center;"><strong>Solid Shapes</strong></p> </td> <td> <p style="text-align: center;"><strong>No. of. Vertices</strong></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Triangular Prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">6</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Cube</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">8</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Rectangular prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">8</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Pentagonal Prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">10</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Hexagonal Prism</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">12</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Triangular Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">4</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Square Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">5</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Pentagonal Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">6</span></p> </td> </tr> <tr> <td> <p style="text-align: center;"><span style="font-weight: 400;">Hexagonal Pyramid</span></p> </td> <td> <p style="text-align: center;"><span style="font-weight: 400;">7</span></p> </td> </tr> </tbody> </table> <h2><span style="font-weight: 400;">Geometry Related Articles</span></h2> <table class="table-bordered"> <tbody> <tr> <td><a href="https://byjus.com/maths/2d-shapes/"><span style="font-weight: 400;">2D Shapes</span></a></td> <td><a href="https://byjus.com/maths/3d-shapes/"><span style="font-weight: 400;">3D Shapes</span></a></td> <td><a href="https://byjus.com/maths/acute-angle/"><span style="font-weight: 400;">Acute Angle</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/acute-angle-triangle/"><span style="font-weight: 400;">Acute Angle Triangle</span></a></td> <td><a href="https://byjus.com/maths/annulus/"><span style="font-weight: 400;">Annulus</span></a></td> <td><a href="https://byjus.com/maths/area-of-shapes/"><span style="font-weight: 400;">Area Of Shapes</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/cardioid/"><span style="font-weight: 400;">Cardioid</span></a></td> <td><a href="https://byjus.com/maths/centroid-of-a-triangle/"><span style="font-weight: 400;">Centroid of a Triangle</span></a></td> <td><a href="https://byjus.com/maths/circles/"><span style="font-weight: 400;">Circles in Maths</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/collinear-points/"><span style="font-weight: 400;">Collinear Points</span></a></td> <td><a href="https://byjus.com/maths/cone/"><span style="font-weight: 400;">Cone</span></a></td> <td><a href="https://byjus.com/maths/congruence-of-triangles/"><span style="font-weight: 400;">Congruence of Triangles</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/conic-sections/"><span style="font-weight: 400;">Conic Sections</span></a></td> <td><a href="https://byjus.com/maths/cube/"><span style="font-weight: 400;">Cube</span></a></td> <td><a href="https://byjus.com/maths/cylinder/"><span style="font-weight: 400;">Cylinder</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/dodecagon/"><span style="font-weight: 400;">Dodecagon</span></a></td> <td><a href="https://byjus.com/maths/ellipse/"><span style="font-weight: 400;">Ellipse</span></a></td> <td><a href="https://byjus.com/maths/equilateral-triangle/"><span style="font-weight: 400;">Equilateral Triangle</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/faces-edges-and-vertices/"><span style="font-weight: 400;">Faces, Edges and Vertices: 3D Shapes</span></a></td> <td><a href="https://byjus.com/maths/frustum-of-cone/"><span style="font-weight: 400;">Frustum Of A Cone</span></a></td> <td><a href="https://byjus.com/maths/frequency-polygons/"><span style="font-weight: 400;">Frequency Polygons</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/geometry-symbols/"><span style="font-weight: 400;">Geometry Symbols</span></a></td> <td><a href="https://byjus.com/maths/heptagon/"><span style="font-weight: 400;">Heptagon</span></a></td> <td><a href="https://byjus.com/maths/hyperbola/"><span style="font-weight: 400;">Hyperbola</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/isosceles-triangle/"><span style="font-weight: 400;">Isosceles Triangle</span></a></td> <td><a href="https://byjus.com/maths/lines/"><span style="font-weight: 400;">Lines</span></a></td> <td><a href="https://byjus.com/maths/locus/"><span style="font-weight: 400;">Locus</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/obtuse-angle/"><span style="font-weight: 400;">Obtuse Angle</span></a></td> <td><a href="https://byjus.com/maths/orthocenter/"><span style="font-weight: 400;">Orthocenter</span></a></td> <td><a href="https://byjus.com/maths/parallelepiped/"><span style="font-weight: 400;">Parallelepiped</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/parallelogram/"><span style="font-weight: 400;">Parallelogram</span></a></td> <td><a href="https://byjus.com/maths/perimeter/"><span style="font-weight: 400;">Perimeter</span></a></td> <td><a href="https://byjus.com/maths/polygon/"><span style="font-weight: 400;">Polygon</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/prism/"><span style="font-weight: 400;">Prism</span></a></td> <td><a href="https://byjus.com/maths/pyramid/"><span style="font-weight: 400;">Pyramid</span></a></td> <td><a href="https://byjus.com/maths/quadrilateral/"><span style="font-weight: 400;">Quadrilateral</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/rectangle/"><span style="font-weight: 400;">Rectangle</span></a></td> <td><a href="https://byjus.com/maths/rhomboid/"><span style="font-weight: 400;">Rhomboid</span></a></td> <td><a href="https://byjus.com/maths/rotational-symmetry/"><span style="font-weight: 400;">Rotational Symmetry</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/scalene-triangle/"><span style="font-weight: 400;">Scalene Triangle</span></a></td> <td><a href="https://byjus.com/maths/sector-of-a-circle/"><span style="font-weight: 400;">Sector Of A Circle</span></a></td> <td><a href="https://byjus.com/maths/solids/"><span style="font-weight: 400;">Solids</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/sphere/"><span style="font-weight: 400;">Sphere</span></a></td> <td><a href="https://byjus.com/maths/square/"><span style="font-weight: 400;">Square</span></a></td> <td><a href="https://byjus.com/maths/triangles/"><span style="font-weight: 400;">Triangles</span></a></td> </tr> <tr> <td><a href="https://byjus.com/maths/trigonometry/"><span style="font-weight: 400;">Trigonometry</span></a></td> <td><a href="https://byjus.com/maths/trigonometry-graphs/"><span style="font-weight: 400;">Trigonometry Graphs</span></a></td> <td><a href="https://byjus.com/maths/types-of-angles/"><span style="font-weight: 400;">Types Of Angles</span></a></td> </tr> </tbody> </table> <h2>Video Lesson</h2> <div class="row"> <div class="col"> <h3 class="text-center">Combination to form Geometry Models</h3> <div class="youtube-video" data-video-thumbnail=""><img class="tumbnailYT" title="Combination to form Geometry Models" src="https://cdn1.byjus.com/wp-content/uploads/2021/05/Combination-to-form-Geometry-Model.jpg" alt="" data-video="https://www.youtube.com/embed/p6DxR2wgmSE" /></div> </div> <div class="faq-section mb30" id="Frequently-Asked-Questions-of-Geometry"><h2><span class="faq-heading">Frequently Asked Questions of Geometry</span></h2><div class="faq-schema"><div itemscope="" itemtype="https://schema.org/FAQPage"><section class="faq-item" itemscope="" itemprop="mainEntity" itemtype="https://schema.org/Question"><div class="faq-num">Q1 </div><div class="faq-rhs"><h3 class="faq-item-ques" itemprop="name">How geometry is used?</h3><div itemprop="acceptedAnswer" itemscope="" itemtype="https://schema.org/Answer"><div itemprop="text"> <p>Geometry is used in configuring and measurement of different shapes and sizes, such as circles, squares, cubes, triangles, etc.</p> </div></div></div></section><section class="faq-item" itemscope="" itemprop="mainEntity" itemtype="https://schema.org/Question"><div class="faq-num">Q2 </div><div class="faq-rhs"><h3 class="faq-item-ques" itemprop="name">What are all the Geometry applications?</h3><div itemprop="acceptedAnswer" itemscope="" itemtype="https://schema.org/Answer"><div itemprop="text"> <p>Geometry has wide usage in daily life. Its major applications are in the field of constructions, such as the construction of building, roads, dams, bridges, etc. and also in surveying, mapping, navigation. In software industries, it is used in graphics designing, gaming, animations, etc. In the medical field as well, for CT scanning and MRI’s geometry concepts are used.</p> </div></div></div></section><section class="faq-item" itemscope="" itemprop="mainEntity" itemtype="https://schema.org/Question"><div class="faq-num">Q3 </div><div class="faq-rhs"><h3 class="faq-item-ques" itemprop="name">Why geometry is important?</h3><div itemprop="acceptedAnswer" itemscope="" itemtype="https://schema.org/Answer"><div itemprop="text"> <p>In our lives, geometry is important to understand the various shapes and measure them based on area and volumes.</p> </div></div></div></section><section class="faq-item" itemscope="" itemprop="mainEntity" itemtype="https://schema.org/Question"><div class="faq-num">Q4 </div><div class="faq-rhs"><h3 class="faq-item-ques" itemprop="name">What geometry means?</h3><div itemprop="acceptedAnswer" itemscope="" itemtype="https://schema.org/Answer"><div itemprop="text"> <p>Geometry means the measurement of Earth, as it derived from the ancient Greek words, ‘geo’ means Earth and ‘metron’ means measurement. So any object which is present on earth has a shape which is defined by geometry.</p> </div></div></div></section></div></div></div> </div>  <div class="clearfix sdsd"></div> </article>  <div class="clearfix"></div> <div id="interactive-quiz-ias-section"> <div id="interactive-quiz-ias" class="interactive-quiz-ias mb20" data-interactive-quiz-name="SinglePageQuiz"> <div id="interactive-quiz-header-ias" class="interactive-quiz-header interactive-quiz-header-ias"> <div class="interactive-quiz-header-ias-popover"> <span tabindex="0" data-toggle="popover" data-trigger="focus" data-placement="bottom" data-content="Select the appropriate option and see your final score and correct answers with solutions at the end of the quiz"> <svg class="svg-img" viewBox="0 0 24 24"> <path fill="currentColor" d="M13,13H11V7H13M13,17H11V15H13M12,2A10,10 0 0,0 2,12A10,10 0 0,0 12,22A10,10 0 0,0 22,12A10,10 0 0,0 12,2Z" /> </svg> </span> <span>Take a quick test on Geometry</span> <div class="question-count active-carousel-item-count question-no-header hidden"> <span class="text">Q</span><span class="badge class value">5</span> </div> </div> </div> <div class="carousel slide carousel-fade quiz-ias" data-ride="carousel" data-interval="false" style="height:50%;width:100%;"> <div class="carousel-inner"> <div class="item active"> <div class="col-md-4 text-center"> <img class="interactive-quiz-ias-img" src="https://cdn1.byjus.com/byjusweb/img/interactive-quiz/Quiz_cartoon.png" alt="Quiz Image"> </div> <div class="col-md-8 text-center main-page-header-text"> <p class="mb30">Put your understanding of this concept to test by answering a few MCQs. 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itemprop="image"><img alt="" src="https://cdn1.byjus.com/wp-content/uploads/2023/03/avatar.png" class="avatar avatar-32 photo" height="32" width="32" loading="lazy"></figure> </span> <span class="cb-comment-meta-data"> <span><span class="fn" itemprop="name">Sai Nirjara Pani</span></span> <span class="comment-dateWrapper"> <a class="cb-comment-meta-date" href="https://byjus.com/maths/geometry/#comment-172186"> <div class="date-submitted" data-nosnippet>September 30, 2020 at 4:41 pm</div> </a> </span> </span> </div> <div class="cb-comment-content" itemprop="text"><p>It is a nice app to learn</p> </div> <div class="cb-meta cb-comment-meta-links"> <a rel='nofollow' class='comment-reply-link' href='https://byjus.com/maths/geometry/?replytocom=172186#respond' onclick='return addComment.moveForm( "div-comment-172186", "172186", "respond", "116764" )' aria-label='Reply to Sai Nirjara Pani'>Reply</a> </div> </div> </span> </li>  <span itemscope itemtype="https://schema.org/Comment"> <li 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rel='nofollow' class='comment-reply-link' href='https://byjus.com/maths/geometry/?replytocom=276977#respond' onclick='return addComment.moveForm( "div-comment-276977", "276977", "respond", "116764" )' aria-label='Reply to Valeria'>Reply</a> </div> </div> </span> </li>  <span itemscope itemtype="https://schema.org/Comment"> <li class="comment even thread-even depth-1" id="comment-302516"> <div id="div-comment-302516" class="cb-comment-body"> <div class="cb-meta cb-comment-meta"> <span class="vcard cb-comment-author" itemprop="creator" itemscope itemtype="https://schema.org/Person"> <figure class="cb-comment-gravatar" itemprop="image"><img alt="" src="https://cdn1.byjus.com/wp-content/uploads/2023/03/avatar.png" class="avatar avatar-32 photo" height="32" width="32" loading="lazy"></figure> </span> <span class="cb-comment-meta-data"> <span><span class="fn" itemprop="name">Sanchit</span></span> <span class="comment-dateWrapper"> <a class="cb-comment-meta-date" href="https://byjus.com/maths/geometry/#comment-302516"> <div class="date-submitted" data-nosnippet>July 30, 2021 at 11:48 am</div> </a> </span> </span> </div> <div class="cb-comment-content" itemprop="text"><p>Its is really good app for learning</p> </div> <div class="cb-meta cb-comment-meta-links"> <a rel='nofollow' class='comment-reply-link' href='https://byjus.com/maths/geometry/?replytocom=302516#respond' onclick='return addComment.moveForm( "div-comment-302516", "302516", "respond", "116764" )' aria-label='Reply to Sanchit'>Reply</a> </div> </div> </span> </li> </ol> <div class="lastLineinCommentsRemover" style="background-color: #f1edff; height: 1px; margin-top: -26px;"></div> </div> <div class="clearfix"></div> </div> </div> </div> <div class="content-grid-column fixed-column-content-right"> <div class="aside">  <aside class="sidebar" role="complementary">  <div class="bgc-white p30 mb20 hidden-xs"> <div class="widget search-widget" id="search-widget"> <div 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position: relative; margin-bottom: 20px;} .pdf-download-modal .pdf-download-form .form-group .form-control { position: relative; height: 45.6px;} .pdf-download-modal .pdf-download-form {padding: 10px 25px;} .pdf-download-modal .pdf-download-form .ws-phone-otp button { height: 45.6px; } .pdf-download-modal .ws-phone-otp img { top: 50%; transform: translateY(-50%);} .form-download{ background: transparent linear-gradient(90deg, #8C3FFF 0%, #2B66FE 51%, #0077FE 100%) 0% 0% no-repeat padding-box; color: #FFFFFF; font-size: 20px; width: 250px; margin-left: auto; margin-right: auto; } .form-download img { background: none; height: auto; border: none; box-shadow: none; display: inline-block; margin-bottom: 4px; } .form-download-spacing{ padding: 0px 8px; } .pdf-download-modal .modal-body { padding: 15px 0; } .pdf-download-form .input-error-msg{ font-size: 10px; } select { color: #9e9e9e !important; } </style> <div class="modal modal-global pdf-download-modal fade pdf-download-register-modal" id="pdf-download-register-modal" role="dialog" data-backdrop="static" data-keyboard="false"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header p20"> <button type="button" class="close" data-close-btn data-dismiss="modal"><svg viewBox="0 0 24 24"><path fill="#000000" d="M19,6.41L17.59,5L12,10.59L6.41,5L5,6.41L10.59,12L5,17.59L6.41,19L12,13.41L17.59,19L19,17.59L13.41,12L19,6.41Z" /></svg></button> <h4 class="modal-title">Register with BYJU'S & Download Free PDFs</h4> </div> <div class="modal-body p20"> <form name="download-pdf" class="pdf-download-form" role="form" method="post" action="https://web.mxradon.com/t/FormTracker.aspx" id="pdf-download-register-modal-form" name="contact" enctype="application/x-www-form-urlencoded"> <div class="row"> <div class="col-sm-12"><div class="form-group"> <div class="ws-phone-otp"> <div class="required-asterisk"><span>*</span></div> <input type="text" name="Phone" oninput="MAIN_UTILITIES.phoneValidation(this,'#join-byjus-form-widget')" onchange="MAIN_UTILITIES.phoneValidation(this,'#join-byjus-form-widget')" onblur="MAIN_UTILITIES.phoneValidation(this,'#join-byjus-form-widget')" class="form-control" placeholder="Mobile Number" data-placeholder="Mobile Number" maxlength="10" data-phone-number-input required data-error-message="Enter a valid 10 digit Mobile Number"> <button class="btn" type="button" data-send-otp>Send OTP</button> <img class="hidden" src="https://cdn1.byjus.com/byjusweb/img/right-tick-icon.svg" alt="validated" width="20" height="20" data-otp-validated-img> </div> </div></div> <div class="col-sm-12"><div class="form-group hidden" data-otp-input-field-voice-call-option> <div class="otp-input-field-voice-call-option"> <input name="otp" type="text" data-otp-number-input class="form-control otp-input-field" placeholder="OTP" maxlength="4" size="4" disabled required> <div class="required-asterisk 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<div class="city-auto-suggestions-comment pr" data-city-auto-suggestions-downloadPdf> <div class="required-asterisk"><span>*</span></div> <input type="text" class="form-control" name="mx_City" placeholder="City" autocomplete="on" onchange="MAIN_UTILITIES.cityValidation(jQuery(this),'#join-byjus-form-widget', 'City');this.isValidInput = USER_DETAILS_INPUT_VALIDATORS.cityValidation;this.requiredName = 'City';var ele = jQuery(this);USER_DETAILS_INPUT_VALIDATORS.cityValidation(ele, '', 'City');" oninput="this.isValidInput = USER_DETAILS_INPUT_VALIDATORS.cityValidation;this.requiredName = 'City';var ele = jQuery(this);USER_DETAILS_INPUT_VALIDATORS.cityValidation(ele, '', 'City');" onblur="MAIN_UTILITIES.cityValidation(jQuery(this),'#join-byjus-form-widget', 'City');"> </div> </div> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <div class="form-group"> <div class="required-asterisk"><span>*</span></div> <div class="select-input-box "> <select class="form-control wrapper" name="grade" data-state="" onchange="MAIN_UTILITIES.requiredValidation(this, '#join-byjus-form-widget', 'Grade');" onblur="MAIN_UTILITIES.requiredValidation(this,'#join-byjus-form-widget', 'Grade');"> <option value="" disabled="disabled" selected="">Grade</option> <option value="1">Class 1</option> <option value="2">Class 2</option> <option value="3">Class 3</option> <option value="4">Class 4</option> <option value="5">Class 5</option> <option value="6">Class 6</option> <option value="7">Class 7</option> <option value="8">Class 8</option> <option value="9">Class 9</option> <option value="10">Class 10</option> <option value="11">Class 11</option> <option value="12">Class 12</option> <option value="ias">IAS</option> <option value="cat">CAT</option> <option value="bankexam">Bank Exam</option> <option value="gate">GATE</option> </select> </div> </div> </div> <div class="col-sm-12"> <div class="form-group"> <button data-form-download-btn class="form-control form-download"><img src="https://cdn1.byjus.com/byjusweb/img/landing-pages/utils-icon/download_white_icon.svg" class="form-download-spacing" alt="download-icon">Download Now</button> </div> </div> </div> </div> <input type="hidden" name="Website" value="https://byjus.com/maths/geometry/"> <input type="hidden" class="inputtext" placeholder="Course" data-old-name="Course" data-name="mx_Course" value="K12" data-is-mapped="1" required="required" name="mx_Course"> <input type="hidden" class="inputtext" placeholder="Source_of_lead" data-old-name="Source_of_lead" data-name="mx_Source_of_Lead" value="Pdf Download Pop up" data-is-mapped="1" required="required" name="mx_Source_of_Lead"> <input type="hidden" value="" data-old-name="mx_UTM_Term" data-name="mx_UTM_Term" data-is-mapped="1" name="mx_UTM_Term"> <input type="hidden" value="" data-old-name="mx_UTM_Match_Type" data-name="mx_UTM_Match_Type" data-is-mapped="1" name="mx_UTM_Match_Type"> <input type="hidden" value="" data-old-name="mx_UTM_Network" data-name="mx_UTM_Network" data-is-mapped="1" name="mx_UTM_Network"> <input type="hidden" value="" data-old-name="mx_UTM_Device" data-name="mx_UTM_Device" data-is-mapped="1" name="mx_UTM_Device"> <input type="hidden" value="" data-old-name="mx_UTM_Site" data-name="mx_UTM_Site" data-is-mapped="1" name="mx_UTM_Site"> <input type="hidden" value="" data-old-name="mx_UTM_Ad_Position" data-name="mx_UTM_Ad_Position" data-is-mapped="1" name="mx_UTM_Ad_Position"> <input type="hidden" name="MXHOrgCode" value="24692"> <input type="hidden" name="MXHLandingPageId" value="cee3d888-c911-11e7-9e09-02b09d13b7e6"> <input type="hidden" name="MXHFormBehaviour" value="1"> <input type="hidden" name="MXHOutputMessagePosition" value="0"> <input type="hidden" name="MXHFormDataTransfer" value="0"> <input type="hidden" name="MXHRedirectUrl" value=""> <input type="hidden" name="MXHAsc" value="10"> <input type="hidden" name="MXHFormName" value="contact"> <input type="hidden" name="MXHOutputMessagePosition" value="0"> </form> </div> </div> </div> </div> <style> .youtube-live-video-redirection-modal .youtube-live-video-redirection-form .required-asterisk span { display: inline-block; position: absolute; right: -5px; font-weight: 700; top: -5px; color: #db4d4d; font-size: 10px; } .youtube-live-video-redirection-modal .youtube-live-video-redirection-form .required-asterisk.required-asterisk-for-otp span { right: inherit; left: 122px; } .youtube-live-video-redirection-modal .youtube-live-video-redirection-form .form-group { position: relative; margin-bottom: 20px;} .youtube-live-video-redirection-modal .youtube-live-video-redirection-form .form-group .form-control { position: relative; height: 45.6px;} .youtube-live-video-redirection-modal .youtube-live-video-redirection-form {padding: 10px 25px;} .youtube-live-video-redirection-modal .youtube-live-video-redirection-form .ws-phone-otp button { height: 45.6px; } .youtube-live-video-redirection-modal .ws-phone-otp img { top: 50%; transform: translateY(-50%);} .form-redirection{ background: transparent linear-gradient(90deg, #8C3FFF 0%, #2B66FE 51%, #0077FE 100%) 0% 0% no-repeat padding-box; color: #FFFFFF; font-size: 20px; width: 250px; margin-left: auto; margin-right: auto; } .form-redirection img { background: none; height: auto; border: none; box-shadow: none; display: inline-block; margin-bottom: 4px; } .form-redirection-spacing{ padding: 0px 8px; } .youtube-live-video-redirection-modal .modal-body { padding: 15px 0; } .youtube-live-video-redirection-form .input-error-msg{ font-size: 10px; } select { color: #9e9e9e !important; } .youtube-live-video-redirection-modal { z-index: 3141593 !important; } </style> <div class="modal modal-global youtube-live-video-redirection-modal fade youtube-live-video-redirection-register-modal" id="youtube-live-video-redirection-register-modal" role="dialog" data-backdrop="static" data-keyboard="false"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header p20"> <button type="button" class="close" data-close-btn data-dismiss="modal"><svg viewBox="0 0 24 24"><path fill="#000000" d="M19,6.41L17.59,5L12,10.59L6.41,5L5,6.41L10.59,12L5,17.59L6.41,19L12,13.41L17.59,19L19,17.59L13.41,12L19,6.41Z" /></svg></button> <h4 class="modal-title">Register with BYJU'S & Watch Live Videos</h4> </div> <div class="modal-body p20"> <form name="redirection-youtube-live-video" class="youtube-live-video-redirection-form" role="form" method="post" action="https://web.mxradon.com/t/FormTracker.aspx" id="youtube-live-video-redirection-register-modal-form" name="contact" enctype="application/x-www-form-urlencoded"> <div class="row"> <div class="col-sm-12"><div class="form-group"> <div class="ws-phone-otp"> <div class="required-asterisk"><span>*</span></div> <input type="text" name="Phone" oninput="MAIN_UTILITIES.phoneValidation(this,'#join-byjus-form-widget')" onchange="MAIN_UTILITIES.phoneValidation(this,'#join-byjus-form-widget')" onblur="MAIN_UTILITIES.phoneValidation(this,'#join-byjus-form-widget')" class="form-control" placeholder="Mobile Number" data-placeholder="Mobile Number" maxlength="10" data-phone-number-input required data-error-message="Enter a valid 10 digit Mobile Number"> <button class="btn" type="button" data-send-otp>Send OTP</button> <img class="hidden" src="https://cdn1.byjus.com/byjusweb/img/right-tick-icon.svg" alt="validated" width="20" height="20" data-otp-validated-img> </div> </div></div> <div class="col-sm-12"><div class="form-group hidden" data-otp-input-field-voice-call-option> <div class="otp-input-field-voice-call-option"> <input name="otp" type="text" data-otp-number-input class="form-control otp-input-field" placeholder="OTP" maxlength="4" size="4" disabled required> <div class="required-asterisk required-asterisk-for-otp"><span>*</span></div> </div> </div></div> </div> <div class="hidden" data-remaining-fields-container> <div class="row"> <div class="col-sm-12"> <div class="form-group mb20"> <div class="required"> <div class="required-asterisk"><span>*</span></div> <input type="text" class="form-control" name="FirstName" placeholder="Name" onchange="MAIN_UTILITIES.nameValiadation(this,'#join-byjus-form-widget')" onblur="MAIN_UTILITIES.nameValiadation(this,'#join-byjus-form-widget')"> </div> </div> </div> <div class="col-sm-12"> <div class="form-group mb20"> <div class="required"> <div class="required-asterisk"><span>*</span></div> <input type="email" class="form-control" name="EmailAddress" placeholder="Email" onchange="MAIN_UTILITIES.emailValidation(this,'#join-byjus-form-widget')" onblur="MAIN_UTILITIES.emailValidation(this,'#join-byjus-form-widget')"> </div> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <div class="form-group mb20"> <div class="required"> <div class="city-auto-suggestions-comment pr" data-city-auto-suggestions-youtubeLive> <div class="required-asterisk"><span>*</span></div> <input type="text" class="form-control" name="mx_City" placeholder="City" autocomplete="on" onchange="MAIN_UTILITIES.cityValidation(jQuery(this),'#join-byjus-form-widget', 'City');this.isValidInput = USER_DETAILS_INPUT_VALIDATORS.cityValidation;this.requiredName = 'City';var ele = jQuery(this);USER_DETAILS_INPUT_VALIDATORS.cityValidation(ele, '', 'City');" oninput="this.isValidInput = USER_DETAILS_INPUT_VALIDATORS.cityValidation;this.requiredName = 'City';var ele = jQuery(this);USER_DETAILS_INPUT_VALIDATORS.cityValidation(ele, '', 'City');" onblur="MAIN_UTILITIES.cityValidation(jQuery(this),'#join-byjus-form-widget', 'City');"> </div> </div> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <div class="form-group"> <div class="required-asterisk"><span>*</span></div> <div class="select-input-box "> <select class="form-control wrapper" name="grade" data-state="" onchange="MAIN_UTILITIES.requiredValidation(this, '#join-byjus-form-widget', 'Grade');" onblur="MAIN_UTILITIES.requiredValidation(this,'#join-byjus-form-widget', 'Grade');"> <option value="" disabled="disabled" selected="">Grade</option> <option value="1">Class 1</option> <option value="2">Class 2</option> <option value="3">Class 3</option> <option value="4">Class 4</option> <option value="5">Class 5</option> <option value="6">Class 6</option> <option value="7">Class 7</option> <option value="8">Class 8</option> <option value="9">Class 9</option> <option value="10">Class 10</option> <option value="11">Class 11</option> <option value="12">Class 12</option> <option value="ias">IAS</option> <option value="cat">CAT</option> <option value="bankexam">Bank Exam</option> <option value="gate">GATE</option> </select> </div> </div> </div> <div class="col-sm-12"> <div class="form-group"> <button data-form-redirection-btn class="form-control form-redirection">Watch Now</button> </div> </div> </div> </div> <input type="hidden" name="Website" value="https://byjus.com/maths/geometry/"> 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It will take some time to appear on the page.</span>')),r.attr("disabled",!1).parent().removeClass("hidden"),i.attr("disabled",!1).parent().removeClass("hidden"),s.attr("disabled",!1).parent().removeClass("hidden"),n.attr("disabled",!1).parent().removeClass("hidden"),c||jQuery.ajax({type:"POST",url:USER_DETAILS_CONFIG.apis.userCreateUpdateUrl,data:l,success:function(e){setStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE",JSON.stringify(DEFAULT_USER_DETAILS)),USER_DETAILS_CONFIG.isUserAlreadyExist=!0},error:function(e){console.log(e)}})):"invalid"===a.status&&a.response?(jQuery(d).text("Post Comment"),jQuery(".form-submit").after('<span class="cb-error-msg">Invalid Comment or User posted too many Comments</span>')):"failed"===a.status&&a.response?(jQuery(d).text("Post Comment"),jQuery(".form-submit").after('<span class="cb-error-msg">Something went wrong, please refresh the page and try again</span>')):(jQuery(d).attr("disabled",!1).text("Post Comment"),jQuery(".form-submit").after('<span class="cb-error-msg">Invalid Comment or User posted too many Comments</span>'))}else jQuery(d).attr("disabled",!1).text("Post Comment"),jQuery(".form-submit").after('<span class="cb-error-msg">Something went wrong. 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Number</div>'))})),getInputAccordingSessionID(e,t,l,m,r,i,n,s),t.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.phoneValidation(this)}),o.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.requiredValidation(this,"","Comment ")}),r.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.nameValiadation(this)}),i.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.emailValidation(this)}),s.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.requiredValidation(this,"","Grade")}),n.on("input",function(){this.isValidInput=USER_DETAILS_INPUT_VALIDATORS.cityValidation,this.requiredName="City";var e=jQuery(this);USER_DETAILS_INPUT_VALIDATORS.cityValidation(e,"","City")}),n.on("change",function(){this.isValidInput=USER_DETAILS_INPUT_VALIDATORS.cityValidation,this.requiredName="City";var e=jQuery(this);USER_DETAILS_INPUT_VALIDATORS.cityValidation(e,"","City")})}}function addGAEvent(e,a){e?GA_FLAG&&ga("send","event","Post Comment Successful","Post Comment activity "+a+" By Existed User","URL: "+C_URL):GA_FLAG&&ga("send","event","Post Comment Successful","Post Comment activity "+a+" By New User","URL: "+C_URL)}function getInputAccordingSessionID(e,a,t,r,i,s,n,o){var d,l;if(null!==getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")&&(d=JSON.parse(getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")),l=d.sessionId,sessionIDSec=d.sessionIdSecondary,void 0!==l&&"undefined"!=typeof sessionIDSec)){var m={session_id:l,session_id_secondary:sessionIDSec};jQuery.ajax({type:"POST",url:USER_DETAILS_CONFIG.apis.userChecBySessionIDUrl,data:m,success:function(e){e.success&&(a.val(e.data.mobile).attr("disabled",!0),t.addClass("hidden"),r.removeClass("hidden"),i.val(e.data.name).attr("disabled",!1).parent().removeClass("hidden"),s.val(e.data.email).attr("disabled",!1).parent().removeClass("hidden"),n.val(e.data.city).attr("disabled",!1).parent().removeClass("hidden"),o.val(e.data.grade).attr("disabled",!1).parent().removeClass("hidden"),MOBILE_OTP_VALIDATER.isPhoneNumberVerified=d.isMobileAlreadyVerified,USER_DETAILS_CONFIG.isUserAlreadyExist=!0,USER_DETAILS_CONFIG.userDetails=e.data)},error:function(e){console.log(e)}})}}var SESSION_ID,SESSION_ID_SECONDARY,DEFAULT_USER_DETAILS={author:"",email:"",mobile:"",isUserAlreadyLoggedIn:!1,isMobileAlreadyVerified:!1,sessionId:"",sessionIdSecondary:"",authorization:"",verifyKey:""},USER_DETAILS_CONFIG={isUserAlreadyExist:!1,apis:{userChecBySessionIDUrl:BASE_URL+"wp-json/spidy/v1/get_user_by_session_id_api/",userCheckUrl:BASE_URL+"wp-json/spidy/v1/user_check_api/?wp-json_allow",userCreateUpdateUrl:BASE_URL+"wp-json/spidy/v1/user_create_update_api/?wp-json_allow",city:{url:BCAP_API_BASE_URL+"api/geo_dimensions/india_state_city_list/?limit="+INDIA_STATE_CITY_LIST_LIMIT_VAL,method:"GET"}},userDetails:""},USER_DETAILS_INPUT_VALIDATORS={getParameterByName:function(e,a){a=a?"?"+a:window.location.search;var t=new RegExp("[?&]"+e.replace(/\[/g,"\\[").replace(/\]/g,"\\]")+"(?:=([^&#]*))?(?:[&#]|$)").exec(a);return t?t[1]?decodeURIComponent(t[1].replace(/\+/g," ")):"":null},requiredValidation:function(e,a,t){var r=jQuery(e),i=r.val(),s="";return 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i=jQuery("[error-section]");jQuery.ajax({type:"POST",url:USER_DETAILS_CONFIG.apis.userCreateUpdateUrl,data:t,success:function(t){!0===t.success?(setStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE",JSON.stringify(DEFAULT_USER_DETAILS)),USER_DETAILS_CONFIG.isUserAlreadyExist=!0,jQuery(e).find("[data-yt-video-widget]")[0].contentWindow.postMessage('{"event":"command","func":"playVideo","args":""}',"*"),a.modal("hide")):jQuery(i).text("Something went wrong. 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u={session_id:s,session_id_secondary:sessionIDSec};jQuery.ajax({type:"POST",url:USER_DETAILS_CONFIG.apis.userChecBySessionIDUrl,data:u,success:function(t){t.success&&(e.val(t.data.mobile).attr("disabled",!0),a.addClass("hidden"),i.removeClass("hidden"),o.val(t.data.name).attr("disabled",!1).parent().removeClass("hidden"),d.val(t.data.email).attr("disabled",!1).parent().removeClass("hidden"),l.val(t.data.city).attr("disabled",!1).parent().parent().removeClass("hidden"),n.val(t.data.grade).attr("disabled",!1).parent().removeClass("hidden"),MOBILE_OTP_VALIDATER.isPhoneNumberVerified=r.isMobileAlreadyVerified,USER_DETAILS_CONFIG.isUserAlreadyExist=!0,USER_DETAILS_CONFIG.userDetails=t.data)},error:function(t){console.log(t)}})}}function appendVideoModalOnBody(){var t='<div class="modal fade video-modal" id="user-detailvideo-widget" role="dialog"';t+='data-backdrop="static" data-keyboard="false">',t+='<div class="modal-dialog">',t+='\t<div class="modal-content">',t+='\t\t<div 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