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Answer: ASA congruency postulate
Step-by-step 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]
- <em>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.</em>
