Ray ak bisects ∠bac, point m ∈ ak so that m∠amb = m∠amc. prove that bk = ck.

Given information: AK bisects ∠BAC, point M ∈ AK so that m∠AMB = m∠AMC.

Prove : BK = CK.

Proof:

In triangle ABM and ACM,

                 (Given)

                  (Reflection property)

                 (Definition of angle bisector)

By SAS postulate,

                            (CPCTC)

It means triangle ABC is an isosceles triangle.

The angle bisector of an isosceles triangle divides the non equal side in two equal parts.

Hence proved.

37.9 im pretty sure

Step-by-step explanation:

you just add all the sides..