In the parallelogram ABCD, the bisector of angle A intersects side BC at point E.
| June 10, 2021 | education
In the parallelogram ABCD, the bisector of angle A intersects side BC at point E. It is known that AB = 12 dm and AD = 17 dm. Calculate the lengths of the segments BE and EC.
1. The angle BAE is equal to the angle DAE, since the bisector AE divides the angle at the vertex A into two equal parts.
2. Angles AEB and DAE are equal as the inner angles lying with parallel lines ВС and АD and secant АЕ. Therefore, the angle BAE = AEB.
3. Triangle ABE is isosceles, since the angles at the base of AE are equal. This means that side AB is equal to side BE. AB = BE = 12 cm.
4. We calculate the length of the segment CE:
CE = BC – BE.
BC = AD = 17 cm.
CE = 17 – 12 = 5 cm.
Answer: the length of the segment BE is 12 cm, the length of the segment CE is 5 cm.
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