In trapezoid ABCD, the bases are 12 cm and 20 cm. Through point M, which lies on the lateral side of AB
September 11, 2021 | education
| 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.
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