In the trapezoid ABCD, the diagonals intersect at the point about Saod

| September 14, 2021 | education

In the trapezoid ABCD, the diagonals intersect at the point about Saod-32cm in the square Sboc-8cm2. Find the smaller base of the trapezoid if the larger one is 10 cm

Consider triangles BOC and AOD.

The BOC angle is equal to the AOD angle as the vertical angles at the intersection of the diagonals, the CBO angle is equal to the ADO angle as the intersecting angles at the intersection of the parallel straight lines BC and AD of the secant BD.

Then the BOC triangle is similar to the AOD triangle in two corners.

The ratio of the areas of similar triangles is equal to the square of the similarity coefficient of the triangles.

Svos / Saod = K2 = 8/32 = 1/4.

K = 1/2.

Then BC / AD = 1/2.

BC = AD / 2 = 10/2 = 5 cm.

Answer: The length of the smaller base is 5 cm.



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