Question

Given that △ABC is an isosceles triangle with AB ≅ AC and AD bisecting ∠BAC, which of the following proves that ∠ABD ≅ ∠ACD?

a) ASA (Angle-Side-Angle) Congruence
b) SAS (Side-Angle-Side) Congruence
c) SSS (Side-Side-Side) Congruence
d) AAS (Angle-Angle-Side) Congruence

Answer 1

The correct option that proves ∠ABD ≅ ∠ACD is (a) ASA (Angle-Side-Angle) Congruence.

Step-by-step explanation:

By the given information, we know that triangle △ABC is isosceles with AB ≅ AC. Since AD bisects ∠BAC, we can split this isosceles triangle into two congruent triangles, △ABD and △ACD.

The reason for this is that the angles opposite the congruent sides are also congruent.

Therefore, the correct option that proves ∠ABD ≅ ∠ACD is (a) ASA (Angle-Side-Angle) Congruence.