The continuation of the lateral sides of the trapezoid ABCD intersect at point O.

The continuation of the lateral sides of the trapezoid ABCD intersect at point O. Find CD if AD = 5cm, BC = 2cm, CO = 6cm.

Since ABCD is a trapezoid, then AD is parallel to BC, and then the angle OBC = OAD as the corresponding angles at the intersection of parallel straight lines BC and AD secant AO.

In triangles AOD and BOC, the angle at the vertex O is common, then triangles AOD and BOC are similar in two angles.

Then from the similarity of triangles: AD / BC = DO / CO.

Let the length DC = X cm, then ОD = (X + 6) cm.

OD = (X + 6) = CO * AD / BC = 6 * 5/2 = 15 cm.

X = OD = 15 – 6 = 9 cm.

Answer: The length of the CD segment is 9 cm.