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<AME = < BMD if AB = CA, BD=//DC, <CDE=60^o, DM=//ME

Source: 2022 Mathematics Regional Olympiad of Mexico West P3

October 6, 2022
equal anglesisoscelesgeometry

Problem Statement

In my isosceles triangle △ABC\vartriangle ABC with AB=CAAB = CA, we draw DD the midpoint of BCBC. Let EE be a point on ACAC such that ∠CDE=60o\angle CDE = 60^o and MM the midpoint of DEDE. Prove that ∠AME=∠BMD\angle AME = \angle BMD.
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