Point M is marked in trapezoid ABCD on the larger base AD so that AM = 3cm, CM = 2cm

univerkov | September 1, 2021 | education

Point M is marked in trapezoid ABCD on the larger base AD so that AM = 3cm, CM = 2cm, angle BAD = angle BCM. Find the lengths of the sides AB and BC.

Consider a quadrangle ABCM, in which the AM side is parallel to the BC side, since AM belongs to AD. The angle BAD, according to the condition, is equal to the angle of the BCM, then the AB side is parallel to the CM side, and therefore the ABCM quadrangle is a parallelogram.

Since the opposite sides of the parallelogram are equal, AB = CM = 2 cm, and BC = AM = 3 cm.

Answer: AB = 2 cm, BC = 3 cm.

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