RD Sharma Chapter 8 Class 9 Maths Exercise 8.4 Solutions

In this article of RD Sharma Chapter 8 Class 9 Maths Exercise 8.4 Solutions, we will explain to students about some new angles made by a transversal with two given lines. This means we will learn about the intersecting two parallel lines. The exercise comprises topics like- alternate interior angles, corresponding angles axiom, and consecutive interior angles. RD Sharma Chapter 8 Class 9 Maths Exercise 8.4 Solutions consists of the Lines and Angles, though the topics mentioned above describes the same in various forms.

The PDF attached to this article has various problems based on the topics that come under Exercise 8.4 of Chapter 8 Class 9. The solution to each question mentioned is provided with a complete explanation and proof. Students will also learn about the tips to understand the question and to solve it efficiently. Students have free access to download the PDF to do the practice.

Download RD Sharma Chapter 8 Class 9 Maths Exercise 8.4 Solutions PDF

Solutions for Class 9 Maths Chapter 8 Lines and Angles Exercise 8.4

Important Definition RD Sharma Chapter 8 Class 9 Maths Exercise 8.4 Solutions

Go down to get the important definition, explanation, and illustrations on the topics-

1. Angles made by a transversal with two lines
2. Alternate interior angles
3. Consecutive interior angles
4. Corresponding angles axiom

When a line converges two lines at distinguished points, it is known as a transversal.

In the figure below, the line ‘n’ is a transversal cutting lines “l’ and ‘m’.

Corresponding Angles

When a transversal cuts two or more lines, the angles which occupy the equivalent relative position are called corresponding angles.

From the above figure, the pairs of corresponding angles are:

1. ∠1 and ∠5
2. ∠2 and ∠6
3. ∠3 and ∠7
4. ∠4 and ∠8

When the lines are parallel, the corresponding angles are congruent.

Consecutive Interior Angles

When a transversal forms two lines, the pairs of angles on one side of the transversal and inside the two lines are known as the consecutive interior angles.

If transversal forms two parallel lines, the pairs of consecutive interior angles made are supplementary.

From the above figure, the consecutive interior angles are-

1. ∠3 and ∠6
2. ∠4 and ∠5

Alternate Interior Angles

When a transversal forms two lines, the pairs of angles on each side of the transversal and inside the two lines are known as the alternate interior angles.

If a transversal forms two parallel lines, the alternate interior angles made are congruent.

From the above figure, the alternate interior angles are-

1. ∠3 and ∠5
2. ∠4 and ∠6

Alternate Exterior Angles

When a transversal forms two lines, the pairs of angles on each side of the transversal and outside the two lines are known as the alternate exterior angles.

If a transversal forms two parallel lines, the alternate exterior angles made are congruent.

From the above figure, the alternate exterior angles are:

1. ∠2 and ∠8
2. ∠1 and ∠7

Frequently Asked Questions (FAQs) of RD Sharma Chapter 8 Class 9 Maths Exercise 8.4 Solutions

Ques 1- How many angles are formed by two lines and a transversal?

Ans- Eight Angles. When a transversal meets with two parallel lines, eight angles are created. The eight angles will unitedly create four pairs of corresponding angles.

Ques 2- What angles are formed by parallel lines?

Ans- The corresponding angles are congruent when the lines are parallel. When a transversal forms two lines, the pairs of angles on each side of the transversal and inside the two lines are known as the consecutive interior angles.

Ques 3- What are two parallel lines cut by a transversal?

Ans- If a transversal cuts two parallel lines, then the pairs of alternate exterior angles are congruent. If a transversal formed two parallel lines, then the consecutive interior angles are supplementary.