The extensions of the lateral sides of the trapezoid ABCD intersect at point O

univerkov | September 8, 2021 | education

The extensions of the lateral sides of the trapezoid ABCD intersect at point O, AD = 5 cm, BC = 2 cm, AO = 25 cm. What is the segment BO equal to?

Since ABCD is a trapezoid, then AD is parallel to BC, and then the angle ОВС = ОАD as the corresponding angles at the intersection of parallel straight lines BC and AD secant AO.

In triangles AOD and BOC, the angle at the vertex O is common, then triangles AOD and BOC are similar in two angles.

Then from the similarity of triangles: AD / BC = AO / VO.

BO = BC * AO / AD.

BО = 2 * 25/5 = 10 cm.

Answer: The length of the segment BО is 10 cm.

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