Question

Prove that the bisectors of the base angles of an isosceles triangle are equal.

Answer 1

An isosceles triangle △ABC with AB = AC

Let:

• AD be the bisector of angle ∠B

• AE be the bisector of angle ∠C

Length of AD = Length of AE

In △ABD and △ACE:

AB = AC     ...(Given)

∠ABD = ∠ACE     ...(Each is half of equal base angles)

∠ADB = ∠AEC     ...(Vertically opposite angles)

By ASA (Angle-Side-Angle) congruence:

△ABD ≅ △ACE ⇒ AD = AE

Proved: AD = AE