The diagonals of the trapezoid ABCD (BC || AD) intersect at point E. find the length CE if AE = 6cm, ED = 4cm. BE = 3cm.

univerkov | February 19, 2021 | education

Let us prove that the triangles BEC and AED are similar.

In triangles BEC and AED, the angle CEB = AED as the vertical angles at the intersection of the diagonals AC and ВD.

Angle ESB = EAD as criss-crossing angles at the intersection of parallel bases of ABP and BC of the secant AC.

Then the triangles BEC and AED are similar in two angles.

From the similarity of triangles:

AE / CE = DE / VE.

CE = AE * BE / DE = 6 * 3/4 = 4.5 cm.

Answer: The length of the CE segment is 4.5 cm.

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