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You have to prove that triangle DBC and traingle ACB are congruent
We know that DC = AB because M is a midpoint for both of them
Look at triangles AMC and DMB now, we know they have 2 sides equal, AM = BM, DM = CM, so definitely AC = DB
Now we know that AC = DB, AB = DC, and BC is a common side between triangles ACB and DBC, by SSS Property, both the traingles are similar and thus share the same angle size, meaning Angle DBC = Angle ACB = 90 degrees
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