BC and AD main trapezoid ABCD angle ABD is equal to the angle BCD. ВС = 4 cm, DC = 6 cm, ВD = 8 cm. Find AD.

univerkov | September 2, 2021 | education

Let us prove that triangles ABD and BCD are similar.

By condition, the angle ABD = BCD, the side BD of the triangles is common.

The angle CBD is equal to the angle ADB as the intersecting angles at the intersection of parallel straight lines BC and AD of the secant BD. Then triangles ABD and BCD are similar in two angles.

Then:

AD / BD = BD / BC.

AD = BD ^ 2 / BC = 64/4 = 16 cm.

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

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