NCERT Solutions for Class 9 Maths Chapter 8

Important NCERT Questions

Quadrilaterals

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 8.1

Page No:146

Questions No: 2

# If the diagonals of a parallelogram are equal, then show that it is a rectangle.

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Given: ABCD is a parallelogram with AC = BD.

To Prove: ABCD is a rectangle.

Solution: In ΔABC and Δ BAD,

BC = AD [∵ Opposite sides of a parallelogram are equal]

AC = BD [∵ Given]

AB = AB [∵ Common]

Hence, ΔABC ≅ ΔBAD [∵ SSS Congruency rule]

∠ABC = ∠BAD [∵ CPCT]

But, ∠ABC + ∠BAD = 180° [∵ Co-interior angles]

⇒ 2∠BAD = 180° [∵ ∠ABC = ∠BAD]

⇒ ∠BAD = 180°/2= 90°

A parallelogram with one of its is 90° is a rectangle. Hence, ABCD is a rectangle.