Question

show that a diagonal divides a square in two congruent triangles

Answer 1

Let ABCD be a square and line AC be its diagonal. We know, in a square all the sides are equal and all the angles are right angled.
So, in ABC and ACD,
AB=CD
angle ABC =angle ADC
AD =BC
So, by SAS congruency both the triangles are equal.

Answer 2

given,

all sides of a square ABCD are equal.

RTP,

Show that a diagonal divides a square into two congruent triangles

Construction:

Join AC
.
proof,

 AB = AD 
BC = DC
AC = AC

By SSS rule, 
Triangle ABC is congruent to triangle ADC. 

hope this aided u,
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