Question

In parallelogram ABCD, one way to prove the opposite sides are congruent is to draw in auxiliary line BD, then prove triangle ABD congruent to triangle CDB, and use CPCTC to prove AD BC and AB DC. Which triangle congruency theorem is used to prove that triangle ABD is congruent to triangle BCD? SSS SAS ASA AAS

Answer 1

The Right answer between the 4 would be ASA

Answer 2

Answer: ASA congruency postulate

Explanation:

Given: Parallelogram ABCD

To prove: ΔABD ≅ ΔBCD

Construction: Draw auxiliary line BD [see in the attachment]

Proof :- In ΔABD and ΔBCD

∠ADB=∠DBC [if lines are parallel, then its alternate interior angles are equal]

BD=BD [common]

∠ABD=∠BDC [if lines are parallel, then its alternate interior angles are equal]

⇒ΔABD ≅ ΔBCD [ASA congruency postulate]

⇒AD=BC and AB=CD [CPCTC]

• ASA postulate tells if two angles and the included side of one triangle are equal to the corresponding parts of another triangle, then the triangles are congruent.