In trapezoid ABCD, the bases are 12 cm and 20 cm. Through point M, which lies on the lateral side of AB

In trapezoid ABCD, the bases are 12 cm and 20 cm. Through point M, which lies on the lateral side of AB, a straight line is drawn parallel to the bases of the trapezoid and intersecting the side CD at point N. Find the length of the segment MN if AM = MB.

Since the segment МН is parallel to the bases, and the lines AB and CD intersect these parallel ones, then the AO Thales theorem CH = DH, and therefore МН is the middle line of the trapezoid.

Then MH = (BC + AD) / 2 = (12 + 20) / 2 = 32/2 = 16 cm.

Answer: The length of the MH segment is 16 cm.