In trapezoid ABCD (AD parallel to BC) BC = 6cm, AD = 14cm, AC = 15cm. E is the intersection of AC and BD. Find CE.

univerkov | May 1, 2021 | education

Consider triangles BCE and ADE, in which the angle BEC = AED as vertical angles, the angle CBE = ADE as criss-crossing angles at the intersection of parallel BC and AD of the secant BD. Then the triangles BEC and CED are similar in two angles.

From the similarity of triangles it follows that: BC / AD = CE / AE.

Let the length of the segment CE be equal to X cm, then AE = (15 – X) cm.

BC / AD = 6 * 14 = X / (15 – X).

14 * X = 90 – 6 * X.

20 * X = 90.

X = AC = 90/20 = 4.5 cm.

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

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.