Question

Given abcd is a rectangle prove the diagonals ac and bd are congruent

Answer 1

Step-by-step explanation:

ab = cd

ad = bc

In triangle abc

angle b=90

By Pythagoras theorem,

ac^2=ab^2+bc^2 -(1)

In triangle bcd

anle c=90

by Pythagoras theorem

bd^2=bc^2+cd^2

but, cd=ab

bd^2=bc^2+ab^2 -(2)

from (1) & (2)

ac^2 = bd^2

taking square root

ac = bd