In trapezoid ABCD (AD || BC) BC = 6cm AD = 14cm AC = 15cm E-point of intersection of AC and BD Find EC

To solve the problem, similar triangles BCE and ADE should be considered. These triangles are similar in the third sign of similarity: the three angles of both triangles are equal, the angles BEC and AED are equal, as vertical, and the angles BDA and CBD, and CAD and BCA, as internal crosswise angles at parallel straight lines ВС and АD.
Let’s compose the following proportions for the sides opposite equal angles, respectively.
BC \ AD = EC \ AE. AE = 15 – EC.
EC \ (15 – EC) = 6 \ 14.
14 * EC = 90 – 6 * EC. 20 * EC = 90.
EC = 90/20 = 4.5.