Ray AK bisects ∠BAC, point M ∈ AK so that m∠AMB = m∠AMC. Prove that BK = CK.
Accepted Solution
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Answer:Given information: AK bisects ∠BAC, point M ∈ AK so that m∠AMB = m∠AMC.Prove : BK = CK.Proof:In triangle ABM and ACM,[tex]\angle AMB\cong \angle AMC[/tex] (Given)[tex]AM=AM[/tex] (Reflection property)[tex]\angle MAB\cong \angle MAC[/tex] (Definition of angle bisector)By SAS postulate,[tex]\triangle AMB\cong \triangle AMC[/tex][tex]AB\cong AC[/tex] (CPCTC)[tex]AB=AC[/tex]It means triangle ABC is an isosceles triangle.The angle bisector of an isosceles triangle divides the non equal side in two equal parts.[tex]BK=CK[/tex]Hence proved.