Question

∆ADB ≅ ∆CDB by the _____

A. AAS Theorem.


B. SSS Postulate.


C. ASA Postulate.


D. SAS Postulate.

Answer 1

Option A is correct

AAS theorem.

Explanation:

AAS(Angle -Angle-Side) theorem states that:

if two angles and any side of one triangle are congruent to two angles and any side of another triangle, then these triangles are congruent

In a given triangle ADB and CDB.

`\angle BAD = \angle BCD` [Angle] [Given]

`\angle BDA = \angle BDC=90^(\circ)` [Angle] [Given]

`BD = BD` {Common side} [Side]

then by AAS theorem;

`\triangle ADB \cong \triangle CDB`

Therefore, ∆ADB ≅ ∆CDB by the AAS theorem.

Answer 2

The marked angles and side BD make up two adjacent angles and a side not between them. The applicable theorem is ...
AAS Theorem