The bases BC and AD of trapezoid ABCD are 9 and 36, respectively, BD = 18. Prove that triangles CBD and ADB

univerkov | August 18, 2021 | education

The bases BC and AD of trapezoid ABCD are 9 and 36, respectively, BD = 18. Prove that triangles CBD and ADB are similar. Can we say that they are similar in 1 similarity feature, because two angles are equal and then write the relationship of the sides?

In the triangles CBD and ADB, the angle CBD = ADB as criss-crossing angles at the intersection of parallel straight lines ВС and АD of the secant ВD.

ВС / ВD = 9/18 = 1/2.

BD / AD = 18/36 = 1/2.

Then the triangles CBD and ADB are similar in two proportional sides and the angle between them, which was required to be proved.

It is not possible to prove the similarity of triangles in two angles.

BC / BD = AD / BD = AB / CD.

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