Question

In the accompanying diagram, line BD bisects acute angle ABC and line AD is parallel to line BC. What kind of triangle must triangle ABD be?

Answer 1

isosceles

Explanation:

With AD║BC, ∠ADB ≅∠DBC. The angle bisection also ensures that ∠ABD≅∠DBC. Hence the two angles ABD and ADB must be congruent to each other.

A triangle with two congruent internal angles is an isosceles triangle.