The bases BC and AD of trapezoid ABCD are respectively (BC) 2 and (AD) 50

univerkov | August 6, 2021 | education

The bases BC and AD of trapezoid ABCD are respectively (BC) 2 and (AD) 50, and the diagonal of BD is 10. Prove that triangles CBD and ADB are similar.

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

BC and BD, BD and AD are similar sides of a triangle.

ВС / ВD = 2/10 = 1/5.

BD / AD = 10/50 = 1/5.

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

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