In a triangle, the median is half the side to which it is drawn. prove that one of the angles of this triangle is equal to the sum of the other two.
Consider the triangle ABC, BM is the median, BM = (1/2) * AC. Consider the isosceles triangles AMB (BM = AM) and BMC (BM = MC). In these triangles, the angles at the bases AB and BC are equal. Let’s write down:
<BAC = <AВM; <MВС = <ВСM.
Now the whole proof boils down to the fact that <B = <ABC = <ABM + <MBC = <BAM + <BCM = <BAC + <BCA, and the angles <BAC and <BCA are the angles at the base of the triangle AC, and in sum they are are equal to the angle at the vertex B.
That is, the angle opposite the larger side of the speaker is equal to the sum of the other two angles.
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