Question

In ΔABC, m∠B = m∠C. The angle bisector of ∠B meets

AC at point H and the angle bisector of ∠C meets AB at point K. Prove that BH = CK.

Answer 1

First, let's illustrate the problem as shown in the picture attached. Then, let's make a two-column proof:

Statement Reason
m∠B = m∠C Given
AB = AC Isosceles Triangle Definition
AK=KB=AH=HC Angle Bisector Postulate
ΔBKC = ΔHBC Line BC is common side
BH = CK Corresponding parts of congruent triangles are congruent