The diagonal AC divides the trapezoid ABCD into two similar triangles ABC and DCA

univerkov | September 16, 2021 | education

The diagonal AC divides the trapezoid ABCD into two similar triangles ABC and DCA. Trapezium base BC = 5cm, AD = 20cm. Find the length of the diagonal AC.

The angle ACB is equal to the angle DAC as the intersecting angles at the intersection of parallel BC and AD secant AC.

Then the AC side of the ABC triangle is similar to the AD side of the DCA triangle, the BC side of the ABC triangle, similar to the AC side of the DCA triangle.

Then BC / AC = AC / AD.

AC ^ 2 = BC * AD = 5 * 20 = 100.

AC = 10 cm.

Answer: The length of the diagonal is 10 cm.

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