In the parallelogram ABCD, the bisector of angle A is drawn, which intersects the side BC at point E. What are the segments BE and EC if AB = 9 cm, AD = 15 cm?
1. The bisector AE of the parallelogram ABCD cuts off the triangle ABE, which is isosceles. Therefore, BE = AB = 9 centimeters.
2. Opposite sides of a parallelogram are equal. Therefore, BC = AD = 15 centimeters.
3. We calculate the length of the CE segment, taking into account that the total length of the CE and BE segments is equal to the length of the BC side:
BE + CE = 15 centimeters.
CE = 15 – 9 = 6 centimeters.
Answer: the segment BE is equal to 9 centimeters, the segment CE is equal to 6 centimeters.
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