Question

Hello ( : could someone help me prove that the diagonals of the rhombus bisect the interior angles?

Answer 1

So far I have : Triangle AED and CED are congruent triangles by the Side-Angle-Side theorem.

Answer 2

Triangles ABD and CBD are congruent by the SSS theorem and therefore
angle ABD = angle CBD

Hence the diagonal bisects angle B.

Same logic for angles D, A and C.

Answer 3

How are they congruent by the SSS postulate?

Answer 4

In rhombus all sides are equal lengths.

AB = CB ; AD = CD ; BD is shared by both triangles.
Three sides of triangle ABD are identical to three sides of triangle CBD and therefore they are congruent.