Question

In ΔABC, AB = AC, BP ⊥ AC and CQ ⊥ AB. ΔABP ≅ ΔACQ by ______.

Options

• RHS

• AAS

• ASA

• SAS

Answer 1

In ΔABC, AB = AC, BP ⊥ AC and CQ ⊥ AB. ΔABP ≅ ΔACQ by RHS.

Explanation:

AB = AC   ...(Given)

BP ⊥ AC and CQ ⊥ AB imply ∠BP and ∠CQ are right angles

Side BP corresponds to CQ perpendicular to the opposite sides

Hypotenuse AB = AC

Thus, ΔABP ≅ ΔACQ by RHS congruence rule.