Question

In the given figure, AD = BC, AC = BD. Prove that ∠ADB = ∠ACB.

Answer 1

Given: AD = BC and AC = BD

To Prove: ∠ADB = ∠ACB

Proof:

1. Consider triangles ΔADB and ΔBCA.

2. In ΔADB and ΔBCA, we have:

AD = BC   ...(Given)

AC = BD   ...(Given)

AB = AB   ...(Common side)

3. By the SSS (Side-Side-Side) congruence criterion, ΔADB ≅ ΔBCA.

4. Therefore, by CPCT (Corresponding Parts of Congruent Triangles), the corresponding angles are equal:

∠ADB = ∠ACB.

Hence proved that ∠ADB = ∠ACB.