Question

Help!!!!! give ton of points

In ΔABC m∠B=m∠C. The angle bisector of ∠B meets AC at point H and the angle bisector of ∠C meetsAB 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