In trapezoid ABCD with base AD = 16 cm, BC = 4 cm, diagonals are drawn that intersect at point O.

| January 18, 2021 | education

In trapezoid ABCD with base AD = 16 cm, BC = 4 cm, diagonals are drawn that intersect at point O. Find the ratio of the areas of triangles AOD and BOC.

Let us prove that the AOD triangle is similar to the BOS triangle.

The angle of the AOD and ВOС in the triangles AOD and ВOС is common, the angle of the AOD is equal to the angle ВCO as the corresponding angles at the intersection of parallel straight lines ABP and BC of the secant ВD.

The ВOС triangle is similar to the AOD triangle in two corners.

Then in such triangles we determine the coefficient of their similarity.

K = BC / BP = 4/16 = 1/4.

The areas of such triangles are referred to as the square of their similarity coefficient.

Svos / Saod = K2 = 1/16.

Saod / Svos = 16.

Answer: The ratio of the areas of the triangles is 16.



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