The bisector of angle A of parallelogram ABCD intersects side BC to point E, find EC if AB = 5cm and AD = 7cm.

Since the segment AE is the bisector of the angle BAD, the angle BAE = DAE.

Angle DAE = AEB as crossing angles at the intersection of parallel AD and BC secant AE, then angle BAE = BEA, and triangle ABE is isosceles, AB = BE = 5 cm.

In a parallelogram, the lengths of the opposite sides are equal, BC = AD = 7 cm, then EC = BC – BE = 7 – 5 = 2 cm.

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




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