Question

In the given figure $\angle{ABC} = \angle{ABD}, BC = BD then \triangle{CAB} =\triangle$___________

• A. ABD
• B. ADB
• C. DAB
• D. DBA

Answer 1

Answer:

C. DAB

To prove the congruence of triangles △CAB and △DAB, let's examine the given information:

• ∠ABC = ∠ABD

• BC = BD

AB is a common side in both triangles △CAB and △DAB.

With these conditions, we can apply the SAS (Side-Angle-Side) Congruence criterion:

• The side AB is common to both triangles.

• The angles ∠ABC and ∠ABD are equal.

• The sides BC and BD are equal.

By SAS, △CAB ≅ △DAB.

Answer: The correct answer is DAB.