On the BC side of the parallelogram ABCD, point M is taken so that AB = BM. a) Prove that AM is the bisector

| September 1, 2021 | education

On the BC side of the parallelogram ABCD, point M is taken so that AB = BM. a) Prove that AM is the bisector of the angle BAD. b) Find the perimeter of the parallelogram if CD = 8 cm, CM = 4 cm.

Since, by condition, AB = BM, the triangle ABM is isosceles, and therefore the angle BAM = BMA. Angle МАD = ВМА as criss-crossing angles at the intersection of parallel straight lines ВС and АD of the secant АМ. Then the angle BAM = MAD, and therefore AM is the bisector of the angle BAD, which was required to be proved.

Since the opposite sides of the parallelogram are equal, AB = CD = 8 cm, and then BM = 8 cm.

The length of the segment BC = AD = BM + CM = 8 + 4 = 12 cm.

Determine the perimeter of the parallelogram. Ravsd = 2 * (AB + AD) = 2 * (8 + 12) = 40 cm.

Answer: The perimeter of the parallelogram is 40 m.



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