Question

Name the postulate or theorem you can use to prove ∆ABD ≅ ∆CBD.

A. SAS Postulate
B. ASA Postulate
C. SSS Postulate
D. AAS Theorem

Answer 1

Hey there!

Triangle CBD is congruent to triangle ABD. This means that BD is congruent to BD by reflexive property. You have two congruent angles, and one congruent side. This would be AAS theorem. The answer is D.

I hope this helps!

Answer 2

Answer:- 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.