Question

In the diagram, AB=BC=CD=DA. prove that triangle ADB is congruent to triangle CBD.

Answer 1

For this problem you will want to use the SSS postulate which is the Side , Side , Side theorem . This means that if you prove three sides of two triangles congruent , then the triangle is congruent . You already know that two sides are congruent , so use the reflexive property and prove DB congruent to DB

Answer 2

Triangle ADB is congruent to triangle CBD. is proved using SSS congruence theorem

How to complete the proof

The two column proof is written as follows

Statement Reason

AB ≅ BC; given

AD ≅ ∠CD given

BD ≅ DB Transitive property

Δ ADB ≅ Δ CBD SSS congruence theorem