On the BC side of the parallelogram ABCD, point M was taken so that AB = BM.

| April 30, 2021 | education

On the BC side of the parallelogram ABCD, point M was 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 – 6 cm.

Let’s connect point A with point M. By condition, AB = BM, then triangle ABM is isosceles, and therefore the angles at the base of AM are equal. Angle BAM = BMA. Angle MAD = BMA as criss-crossing angles at the intersection of parallel straight lines BP and BC of the secant AM, then the angle BAM = MAD, and meaning the segment AM is the bisector of angle A, which was required to be proved.

Since ABCD is a rectangle, then AB = CD = 8 cm. By condition, BM = AB, then BM = 8 cm.

Side length BC = BM + CM = 8 + 6 = 14 cm.

Let’s define the perimeter ABCD.

P = 2 * AB + 2 * BC = 2 * 8 + 2 * 14 = 16 + 28 = 42 cm.

Answer: The perimeter of the rectangle is 42 cm.



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