Question

AO = OD. ΔABO ≅ ΔDCO by ______.

Options

• RHS

• AAS

• SAS

• ASA

Answer 1

AO = OD. ΔABO ≅ ΔDCO by ASA.

Explanation:

Since AO = OD (given) and the two triangles ΔABO and ΔDCO share the common side OD:

1. ∠BAO = ∠DCO  ...(Vertically opposite angles)
2. AO = OD  ...(Given)
3. AB = DC  ...(As both are sides of the same triangle)

Thus, the triangles are congruent by the ASA (Angle-Side-Angle) criterion, as two angles and the included side in one triangle are congruent to the corresponding angles and included side of the other triangle.