RD Sharma Chapter 15 Class 9 Maths Exercise 15.1 Solutions is about Figures on the same base and between the same parallels, which is concerned under the Area of Parallelograms and Triangles. This theory helps students distinguish figures that lie on the same base and between the same parallel that will help solve complicated problems of the exercise.

Check the attached RD Sharma Chapter 15 Class 9 Maths Exercise 15.1 Solutions PDF, which helps students to solve several types of questions based on this exercise. Practicing with the PDF help to score well in the exam as it is prepared by the professionals through the RD Sharma and CBSE Text Book of Class 9.

**Learn about RD Sharma Class 9 Chapter 15 (Areas Of Parallelograms And Triangles)**

Table of Contents

## Download RD Sharma Chapter 15 Class 9 Maths Exercise 15.1 Solutions PDF

Solutions for Class 9 Maths Chapter 15 Area of Parallelogram and Triangles Exercise 15.1

## Important Definitions RD Sharma Chapter 15 Class 9 Maths Exercise 15.1 Solutions

**Figures on the same base and between the same parallels**

Two geometric diagrams are said to be on the same base and among the same parallels if they have a subordinate side as base and vertices opposite to the common base that lies on the line parallel to the base.

**Example of RD Sharma Chapter 15 Class 9 Maths Exercise 15.1 Solutions**

Ques- Which of the following figures lie on the same base and between the same parallel. In such a case, write the common base and two parallels-

Solution- (i) Triangle APB and trapezium ‘ABCD’ are on the subordinate base ‘AB’ and between the same parallels AB and DC.

So,

Common base ‘AB’

Parallel lines are ‘AB and DC’

(ii) Parallelograms ‘ABCD’ and ‘APQD’ are on the corresponding base ‘AD’ and between the corresponding parallels’ AD and BQ’.

Common base ‘AD’

Parallel lines are ‘AD and BQ’

(iii) Consider, parallelogram ‘ABCD’ and ‘ΔPQR’, lies within the same parallels’ AD’ and ‘BC’. But not sharing a common base.

(iv) ‘ΔQRT’ and parallelogram ‘PQRS’ are on the same base, ‘QR’ and lies between the same parallels’ QR and PS’.

Common base ‘QR’

Parallel lines are ‘QR and PS’

(v) Parallelograms’ PQRS’ and trapezium ‘SMNR’ share a common base ‘SR’, but not between the same parallels.

(vi) Parallelograms are PQRS, AQRD, BCQR are among the same parallels. Also,

Parallelograms are PQRS, BPSC, APSD are within the same parallels.

## Frequently Asked Questions (FAQs) of RD Sharma Chapter 15 Class 9 Maths Exercise 15.1 Solutions

Ques 1- Which parallelograms have the same area?

Ans- Because the parallelogram and rectangle are formed of the same parts, they necessarily have the equivalent area.

Ques 2- Does a parallelogram have four right angles?

Ans- Yes, Rectangle is an example of a parallelogram with four right angles.

Ques 3- Are all sides of a parallelogram equal?

Ans- A parallelogram has opposite sides parallel and equivalent in length. Also, opposite angles are the same (angles “A” are the same, and the angles “B” are the same).

Ques 4- How do you find the angles in a parallelogram?

Ans- There are six major properties of parallelograms-

- The opposite sides are congruent (PQ = RS).
- Opposite angles are congruent (S = Q).
- Consecutive/ Adjacent angles are supplementary (P + S = 180°).
- If one angle is right, then all angles are also right.
- The diagonals of a parallelogram bisect (divide) each other.
- Each diagonal of a parallelogram divides it into two adjacent/ congruent triangles.