Name the postulate or theorem you can use to prove ∆abd ≅ ∆cbd.
a. sas postulate
b. asa postulate
c. sss postulate
d. aas theorem

- D) AAS Theorem

Explanation:-

Given :- Δ ADC where ∠A=∠C , ∠ABD=90° which means Bd is an altitude .

⇒∠CBD =90° [∵∠ABD+∠CBD=180° linear pair]

Proof :- In  ∆ABD and ∆CBD.

∠A=∠C [given]..> angle

∠ABD=∠CBD [right angle]..> angle

BD=BD [Reflexive property]..> side

⇒ ∆ABD ≅ ∆CBD [by AAS congruence theorem]

AAS congruence theorem tells that if two angles and one side of a triangle is congruent to the two angles and one side of a triangle then the triangles are congruent.

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