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: 3

# Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

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Given: ABCD is a quadrilateral in which AO = CO, BO = DO and ∠COD = 90°.

To prove: ABCD is a rhombus.

Sulution: In ΔAOB and ΔAOD,

BO = DO [∵ Given]

∠AOB = ∠AOD [∵ Each 90°]

AO = AO [∵ Common]

Hence, ΔAOB ≅ ΔAOD [∵ SAS congruency rule]

AB = AD [∵ CPCT]

Similarly, AB = BC and BC = CD

Now, all the four sides of Quadrilateral ABCD are equal.

Hence, ABCD is a rhombus.