Triangle Congruence: Proving ΔADB≅ΔCBD with Parallel Lines

Question

AD = BC

AD || BC

According to which theorem are the triangles ΔADB≅ΔCBD congruent?

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Step-by-Step Solution

We are given: AD=BC

The angle ADB is equal to the angle CBD since AD is parallel to BC and the corresponding angles are equal between parallel lines.

DB=DB since it is a common side.

Therefore, we have two triangles that are congruent according to the S.A.S. (side, angle, side) theorem.

Answer

According to the S.A.S. theorem