Question

In ||^gm ABCD, BQ and DP are ⊥ AC. ΔADP ≅ ΔCBQ by ______.

Options

• RHS

• ASA

• AAS

• SAS

Answer 1

In ||^gm ABCD, BQ and DP are ⊥ AC. ΔADP ≅ ΔCBQ by AAS.

Explanation:

1. AD = BC  ...(Opposite sides of a parallelogram are equal)
2. ∠DAP = ∠CBQ = 90°  ...(Since BQ and DP are perpendicular to AC)
3. ∠PAD = ∠QBC  ...(Alternate interior angles due to parallel lines)

These satisfy the AAS (Angle-Angle-Side) congruence criterion two angles and a non-included side in one triangle are congruent to two angles and the corresponding side in the other triangle.

Hence, ΔADP ≅ ΔCBQ by AAS.