The extensions of the lateral sides AB and CD of the trapezoid ABCD intersect at point K

univerkov | May 7, 2021 | education

The extensions of the lateral sides AB and CD of the trapezoid ABCD intersect at point K. The smaller base BC is 4 cm, BK = 5 cm AB = 15 cm. Find the larger base of the trapezoid.

Determine the length of the segment AK.

AK = AB + BK = 15 + 5 = 20 cm.

Consider a triangle AKD and BKC, in which the angle at the vertex A is common, the angle KBC = KAD as the corresponding angles at the intersection of parallel lines AD BC secant AK.

Then triangles AKD BKC are similar in two angles.

Then in similar triangles: BC / AD = BK / AK.

AD = BC * AK / BK = 4 * 20/5 = 16 cm.

Answer: The length of the AD base is 16 cm.

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