In the parallelogram ABCD, AE is the bisector of angle A. The sides of the parallelogram AB and BC are related as 4: 9.

univerkov | April 30, 2021 | education

In the parallelogram ABCD, AE is the bisector of angle A. The sides of the parallelogram AB and BC are related as 4: 9. AE intersects the diagonal BD at point K. Find the ratio BK: KD.

Let the length of the side AB = 4 * X cm, then, by condition, the length of the side BC = 9 * X cm.

Since AE is the bisector of the angle BAD, then by the property of the bisector triangle ABE is isosceles, in which BE = AB = 4 * X cm.

Triangles BKE and AKD are similar in two angles. Angle BKE = AKD as vertical, angle BEC = KAD as lying cross at the intersection of parallel straight lines.

Then, in similar triangles:

BE / AD = BK / KD.

ВK / KD = 4 * X / 9 * X = 4/9.

Answer: The ratio ВK / KD = 4/9.

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