Question

BD bisects ∠ABC. ΔABD ≅ ΔCBD by ______.

Options

• SAS

• RHS

• AAS

• ASA

Answer 1

BD bisects ∠ABC. ΔABD ≅ ΔCBD by AAS.

Explanation:

Since BD bisects ∠ABC, it divides the angle into two equal parts, meaning:

• ∠ABD = ∠CBD  ...(By the angle bisector property)
• Also AB = BC ...(Since both triangles share the side AB and BD bisects the angle)
• BD = BD  ...(Common side)

With two angles and the included side of one triangle equal to two angles and the included side of the other triangle, ΔABD ≅ ΔCBD by the AAS (Angle-Angle-Side) congruence criterion.