The bisector of angle A of parallelogram ABCD intersects side BC at point K. Find KC if AB = 5 cm and AD = 7 cm.

univerkov | May 23, 2021 | education

Since ABCD is a parallelogram, its opposite sides are equal and parallel.

Then the angle DАК = ВКА as criss-crossing angles at the intersection of parallel straight lines АD and ВС secant АС.

Then in the triangle AВK the angle ВAK = ВKA, which means that the triangle AВK is isosceles, ВK = AB = 5 cm.

BC = AD = 7 cm.

Then KС = ВС – ВK = 7 – 5 = 2 cm.

Answer: The length of the CК segment is 2 cm.

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