Question

prove that each of the diagonals of a square divides it into two congruent triangles

Answer 1

Consider square abcd with bd as diagonal.

Consider triangle abd, triangle cdb

Angle a=angle c=90(since it is a square all angles are 90)

Bd=bd(common)

Ab=dc(all sides are equal in a square)

Therefore triange abd congruent to triangle cdb by rhs criteria.