In parallelogram ABCD, the bisector of angle A is drawn, which intersects the side BC

In parallelogram ABCD, the bisector of angle A is drawn, which intersects the side BC at point E. Find the lengths of the segments BE and EC if AB = 9cm, AD = 15cm

1. The ВAD angle is equal to the EAD angle, since the bisector of angle A divides it in half.

2. The angle EAD is equal to the angle AEB as the internal cross-lying angles at two parallel

straight lines AD and BC and secant AE.

3. Consequently, the angle BAE is equal to the angle AEB, that is, triangle ABE is isosceles and

sides AB and BE are equal:

AB = BE = 9 centimeters.

4. We calculate the length of the segment EC:

15 – 9 = 6 centimeters.

Answer: the length of the segment BE is 9 centimeters, the length of the segment CE is 6 centimeters.