CBSE Class 9 Maths Revision Notes Chapter 8

Class 9 Mathematics Revision Notes for Quadrilaterals of Chapter 8

The Class 9 Mathematics Notes provided by Extramarks are ideal for students who want to gain more knowledge and command of the subject. Class 9 Mathematics Quadrilaterals Notes are prepared by subject matter professionals and thoroughly revised with advanced concepts. The notes have detailed explanations and precise notes for each concept to help students understand it better.

Parallelograms:

• An equal and opposite parallel pair of sides make up a parallelogram, a quadrilateral.
• Rectangles, rhombuses, and squares make up parallelograms.
• A trapezium is a quadrilateral with a single pair of parallel opposite sides. It does not consequently create a parallelogram.
• All pairs have equal and parallel opposite sides.

• Opposite sides are two sides of a quadrilateral that share no common point.
• AB and DC are one pair of opposite sides in the diagram.
• The other pair of opposite sides is DC and BC.

• Consecutive sides are two sides of a quadrilateral that share an endpoint.
• As shown in the diagram,
• AB and BC are two consecutive sides.
• The other three sets of successive sides are BC, CD; CD, DA; and DA, AB.

• The opposite angles of a quadrilateral are two angles that intersect but do not comprise a side.
• As shown in the diagram,
• One set of opposite angles is ∠A and ∠C, while another pair of opposite angles is ∠B and ∠D.

• The intersection of two quadrilateral angles that comprise a side is known as a consecutive angle.
• As shown in the diagram,
• ∠A and ∠B are one pair of successive angles, while the other three pairs are ∠B, ∠C; ∠C, ∠D; and ∠D, ∠A.

Sufficient Conditions for a Quadrilateral to be a Parallelogram:

• The following is the defining property of a parallelogram:
• “The opposite sides of a quadrilateral are equal if it is a parallelogram.”

Special Parallelograms:

Parallelograms are made up of rectangles, rhombuses, and squares.

Here are some possible definitions for each of these:

• A is an equilateral and equiangular parallelogram. As a result, a square can be a rectangle as well as a rhombus.
• The graphic below depicts the relationships between the special parallelograms:
• As every rectangle and rhombus would be a parallelogram, they are represented as subsets of a parallelogram, while a square is represented by the overlapping shaded area because it is both a rectangle and a rhombus.

Rectangle:

A rectangle is a parallelogram with a right angle at one of its corners.

In the above figure,

Let, ∠A=90

Since,

∠A+ ∠B=180

(Sum of interior angles along the same transverse AB side)

Therefore,

∠B=90

Here,

AB∥CD and ∠A=90 (Given)

Therefore,

∠A+∠D=180

∴∠D=90

∴∠C=90

Corollary: Each of a rectangle’s four angles is a right angle.

Rhombus:

A parallelogram with two successive equal sides is known as a rhombus.

ABCD  is a rhombus in which AB=BC.

Since a rhombus is a parallelogram,

Corollary: A rhombus’s four sides are all equal (congruent).

Square:

A square is a rectangle that has two sides of the same length on consecutive sides.

Since a square is a rectangle,

AB=DC and BC=CD are true since every angle of a rectangle is a right angle.

A square has four equal-length sides and four right angles, all of which are the same length.

Class 9 Mathematics Quadrilaterals Notes Free

Extramarks’ Quadrilaterals Class 9 Notes are written by subject matter experts, ensuring that students access reliable and accurate notes from one place. They can read and understand it at their leisure, as it is easily available from the website of Extramarks. Furthermore, the notes are available in both English and Hindi to ensure that students fully comprehend the concepts. They can also refer to these notes for competitive exams. In addition, class-wise notes are available for all chapters of all subjects.

The chapter begins with a review of triangles which are made up of three angles. Similarly, a quadrilateral is a shape made up of four angles and four sides of varying lengths. These figures have specific qualities, which will be explored further in the chapter. Certain objects, such as a chalkboard, book, or table, can be used as examples for quadrilaterals to help students understand these figures.

• Polygons are planar figures with sides defined by straight-line segments that we are all familiar with.
• The term polygon is derived from Greek.
• It refers to a figure with many angles, implying many sides.
• Quadrilaterals are four-sided geometric shapes formed by the union of four line segments.
• A quadrilateral is a four-sided polygon.

Angle Sum Property of The Quadrilateral

In this section, one of the basic features of the quadrilateral ‘additive property’ is explained. According to this property, the total of all quadrilateral angles equals 360°. It denotes a complete circle angle.

Students are familiar with a quadrilateral and its angle sum property. In this section, they will learn more about quadrilaterals and their different varieties. According to Chapter 8 of Class 9 Mathematics Notes, there are five major varieties of quadrilaterals. They are:

• The trapezium is a quadrilateral figure that has a single pair of parallel sites.
• A parallelogram is a form of a quadrilateral in which both pairs are parallel to one another.
• A rectangle is the third type of quadrilateral. It has four right angles and two equal corresponding sides.
• A rhombus is a quadrilateral with all four sides equal.
• A square is a quadrilateral that includes the characteristics of both a rectangle and a rhombus. It has four equal sides and 90° angles.

Properties of Parallelogram

This section explains the different properties of parallelograms with theorems and proofs. A parallelogram’s attributes are as follows:

• A parallelogram’s diagonal can be used to divide into two congruent triangles.
• The opposite sides of a parallelogram are equal.
• It is similar to the previous property. If the opposite sides of a quadrilateral are equal, the quadrilateral is said to be a parallelogram.
• The parallelogram has another property known as opposite angles equal.
• If two diagonals in a parallelogram are drawn, they will bisect each other.
• The quadrilateral is known as a parallelogram if the above-mentioned criterion is satisfied and the diagonals are likewise bisected.
• When the diagonals are drawn in a rhombus, they are perpendicular to each other.

Another Condition For A Quadrilateral To Be A Parallelogram

Another criterion for a quadrilateral to be a parallelogram is that if a figure of quadrilaterals with opposite sides is equal and parallel to each other, it is a parallelogram. So far, it was assumed that any of the conditions can be met; however, there is now an extra condition that meets both criteria.

Midpoint Theorem

In this final section, students are introduced to a new theorem called the midpoint theorem. It explains that if a line segment connects two sides of a triangle; it is parallel to the third side of the triangle. A diagram makes it simple to demonstrate this. Class 9 Mathematics Chapter 8 Notes additionally provides an explanation of the converse of the theorem. This theorem is also known as the exact midpoint theorem. This theorem states that the line extended to the middle of one triangle’s side is parallel to the other side and cuts the third side in half.

A quadrilateral is a figure that is formed by combining four non-collinear parts. It is defined as a four-sided polygon, or a figure made by connecting collinear points so that the shape has four sides, four vertices, and two diagonals. The total of the angles in the quadrilateral is 360 degrees. The different four-sided polygons include square, rectangle, rhombus, parallelogram, and trapezium.

2. What is the relation between a trapezium and a parallelogram?

All trapeziums are parallelograms, but not all parallelograms are trapeziums.

3. How do the shapes of squares, rectangles, and rhombus relate to one another?

Rhombus and rectangle and square all have four sides and are classified as quadrilaterals. However, rhombuses and rectangles are not squares.

4. What advantages do Class 9 Chapter 8 Mathematics notes offer?

Chapter 8 of the Class 9 Mathematics notes are designed to help students cover and concentrate on the chapter’s most crucial topics. In the chapter titled “Quadrilaterals,” students are taught the necessary kinds of quadrilaterals and their many properties. These notes were created by subject matter experts and are written in simple language. Students will be able to learn more with a step-by-step explanation of all the topics.

5. How many different types of quadrilaterals are there?

Students are exposed to numerous four-sided polygons and their properties in Chapter 8 Class 9, which is devoted to quadrilaterals. As a result, Class 9 students are introduced to a total of 6 different types of quadrilaterals. The quadrilaterals that are described include:

• Trapezium
• Parallelogram
• Rectangle
• Rhombus
• Square
• Kite