Home/ Questions/Q 2096
Next
Answered
Nitya Singh
  • 6
Asked: 2020-11-03T09:56:28+00:00 In:

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

  • 6

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

2020-2021cbsechapter 8class 9mathematicsncertquadrilaterals
Share

    2 Answers

    1. Get Hindi Medium and English Medium NCERT Solution for Class 9 Maths to download.
      Please follow the link to visit website for first and second term exams solutions.
      https://www.tiwariacademy.com/ncert-solutions/class-9/maths/chapter-8/

      • 3
    2. Best Answer
      Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

      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.

      • 1
    Leave an answer

    Leave an answer

    Browse