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

Question

anonymous · Answer

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anonymous · Answer

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

ranga · Answer

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.

anonymous · Answer

How are they congruent by the SSS postulate?

ranga · Answer

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.