# NCERT Solutions for Class 9 Maths Chapter 8 – Quadrilaterals PDF

## Free PDF of NCERT Solutions for Class 9 Maths Chapter 8 – Quadrilaterals

includes all the questions provided in NCERT Books prepared by Mathematics expert teachers as per CBSE NCERT guidelines from wallindia . To download our free pdf of Chapter 8 Quadrilaterals Maths NCERT Solutions for Class 9 to help you to score more marks in your board exams and as well as competitive exams.

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In geometry, a quadrilateral is a closed shape that is formed by joining four points among which any three points are non-collinear. A quadrilateral has 4 sides, 4 angles, and 4 vertices. 'Quadrilateral' is derived from a Latin word, in which, 'Quadra' means four and 'Latus' means sides. All 4 sides of a quadrilateral may or may not be equal.

A quadrilateral is a polygon with four sides four angles and four vertices. Whenever we name a quadrilateral, we need to keep in mind the order of the vertices. For example, the following quadrilateral should be named ABCD, BCDA, ADCB, or, DCBA. It cannot be named as ACBD or DBAC, since they change the order of vertices in which a quadrilateral is formed. The following quadrilateral ABCD has four sides: AB, BC, CD, DA, and two diagonals: AC and BD.

#### Types of Quadrilateral

Although a quadrilateral always has four sides, four angles, and four vertices, the measure of the sides and angles differ. It is to be noted that the sum of the interior angles of a quadrilateral is always equal to 360°.

#### Properties of Quadrilateral

Each of the quadrilateral discussed above has its own properties. Though, there are some properties that are common to all quadrilaterals. They are as follows.

• They have four sides.
• They have four vertices.
• They have two diagonals.
• The sum of all interior angles is 360°.
• We will study the other properties of different quadrilaterals in detail. We can identify a quadrilateral by using the following properties of quadrilaterals.

### Geometric Shapes

Any object around us with a fixed structure can be considered a geometric shape. These shapes are made up of lines, curves, angles, and surfaces. Some of the known geometric shapes are square, rectangle, circle, cylinder, etc. A polygon is a geometric shape with 3 or more sides. Some of the common polygons are triangle, square, rhombus, trapezium, etc.

In this article, we will explore different two-dimensional and three-dimensional geometric shapes and their properties. We will solve a few examples based on them for a better understanding of the concept.

### What are Geometric Shapes?

Geometric shapes are any structure, open or closed, having a definite shape and properties made up of lines, curves and points. Some of the known geometric shapes are square, rectangle, circle, cone, cylinder, sphere, etc. All these shapes have some properties that make them unique and different from the other shapes.

Geometric shapes are defined as figures closed by a boundary which is made by combining the definite amount of curves, points, and line segments. Each shape has a unique name such as circle, square, triangle, rectangle, etc. In real life, we are surrounded by various basic geometric shapes, like the slice of a pizza is in the shape of a triangle, doors or windows are in the shape of a rectangle, and many more.

### Types of Geometric Shapes

In geometry, when an object or a shape is not connected with both ends, it is considered an open geometric shape. When an object or a shape is connected with both ends it is considered a closed geometric shape. There are two types of geometric shapes, classified as:

Two-dimensional: These are 2D shapes that have only the x-axis and y-axis. They are flat structures with 2 dimensions. For example, triangle, square, rectangle, etc.
Three-dimensional: These are 3D shapes that have an x-axis, y-axis, and z-axis. The z-axis represents the height of the object. They are solid structures with 3 dimensions. For example, cube, cuboid, etc.

To draw any of these geometric figures, we have to start with a line, a curve, or a line segment. Thus, based on the number and arrangement of the lines we can make different types of geometric shapes and figures, for example, by joining four line segments a rectangle shape is formed. A triangle can be formed by joining three-line segments and so on.