Question

prove that the diagonal of rectangle divide into two congruent triangle

Answer 1

if abcd is a rectangle and bd is a diagonal.

in triangles abd and cdb :

=) ab = cd
=) bd = bd
ad = cb

by sss congruency criteria ;
both are congruent.

Answer 2

Given:ABCD is a rectangle
AC is the diagonal of the rectangle
RTP:∆ABC congruent to ∆ADC
Proof:
=>AB=DC(Opposite sides of a rectangle are equal)
=>AD=BC(Opposite sides of a rectangle are equal)
=>AC=AC(Common side)
Hence ∆ABC is congruent to ∆ADC(By SSS congruence rule)