In trapezoid ABCD, base BC = 4, AD = 64, diagonal BD = 16. Prove that triangles CBD and ADB are similar.

Let us assume that triangles BCD and ABD are similar.

Angle CBD = ADB as lying crosswise at the intersection of parallel AD and BC.

The BC side of the ВСD triangle is similar to the ВD side of the ABD triangle, then ВС / ВD = 4/16 = 1/4.

The AD side of the ABD triangle is similar to the BD side of the BCD triangle, then BD / AD = 16/64 = 1 / 4. Therefore, the two similar sides of the triangles are proportional, and the angles between them are equal, which means that the CBD and ADB triangles are similar in the second characteristic, as needed to be proved.