Question

In the quadrilateral ABCD, AD = CD and ∠A = 90° = ∠C.

Prove that AB = BC.

Answer 1

Given: In quadrilateral ABCD, AD = CD and ∠A = 90°, ∠C = 90°

To Prove: AB = BC

Proof:

1. Since AD = CD and ∠A = ∠C = 90°, triangles ABD and CBD share the side BD.

2. Consider triangles ABD and CBD:

AD = CD   ...(Given)

∠A = ∠C = 90°   ...(Given)

BD = BD   ...(Common side)

3. By RHS (Right angle-Hypotenuse-Side) congruence criterion, △ABD ≅ △CBD.

4. Therefore, corresponding parts of congruent triangles are equal, so AB = BC.

Hence, in quadrilateral ABCD, AB = BC is proved.