The bisector an and cm are drawn in the parallelogram abcd. Prove that amcn is a parallelogram.

univerkov | August 13, 2021 | education

Since AH and CM are bisectors of the angles, they cut off the isosceles triangles ABН and СDM.

Triangles ABN and CDM are equal on two sides, since AB = CD = DM = BH, and somewhere between them.

Then AH = CM.

Since the opposite sides of the parallelogram are equal, BC = AD, and BH = DM, then the segment CH = AM.

Then in the quadrangle AHCM the opposite sides are pairwise equal, therefore, the quadrilateral is a parallelogram, which was required to prove.

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