Question

Show that the four triangles as shown in the adjoining fig. formed by diagonals and sides of rhombus are congruent.

Answer 1

A rhombus is a parallelogram with four congruent sides.

So, all sides of rhombus ABCD are congruent.

i.e. $AB\cong BC\cong CD\cong AD$

We also know that the diagonals of a parallelogram bisect each other,

Since a rhombus is a parallelogram, it also has this property.

$\therefore BE\cong DE,AE\cong CE$.

$\therefore$ all $4$ triangles are congruent by SSS.