In parallelogram ABDC, a bisector of angle A is drawn, which intersects side BC at point E.

univerkov | September 5, 2021 | education

In parallelogram ABDC, a bisector of angle A is drawn, which intersects side BC at point E. what are the lengths of BE and EC equal to, if AB = 9cm, AD = 15cm?

Angle BAE = angle EAD (AE – bisector, by convention).
Angle BEA = angle EAD (internal criss-crossing angles with parallel lines BC, AD and secant AE), therefore angle BAE = angle BEA.
Consider a triangle ABE, in which two angles are equal, which means that this triangle is isosceles and the sides in it are equal.
AB = BE = 9 cm.
AD = BC = 15 cm (ABCD – parallelogram). Find the segment EC:
EC = BC – BE = 15 – 9 = 6 (cm).
Answer: segment BE = 9 cm, segment EC = 6 cm.

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