I need to figure out this proof, the figure is two triangles forming a rhombus.

Question

Given: segment BD is the angle bisector of triangle ABC and triangle ADC
Prove: Triangle ABD is congruent to Triangle CBD

So far I have segment BD is the angle bisector of triangle ABC and triangle ADC (Given), and segment BD is congruent to segment BD (Reflexive property)... where do I go on from here?

Answer 1

since ABCD is a rhombus, all the sides are equal.

So, we already know that AD=AB=BC=CD
Since BD is an angle bisector,
<ABD = <DBC

So, we have SAS and the triangles are congruent.