The bases of the trapezoid are 20 and 25. find the largest segment of the midline into which one

univerkov | August 15, 2021 | education

The bases of the trapezoid are 20 and 25. find the largest segment of the midline into which one of the diagonals divides it?

Let the segment KM be the middle line of the trapezoid, which the diagonal BD intersects at the point O.

Since KM is the middle line of the trapezoid, it is parallel to the bases of the trapezoid.

In triangle ABD, point K is the middle of side AB, and the segment KO is parallel to the base D, then the segment KO is the middle line of triangle ABD, then KO = AD / 2 = 25/2 = 12.5 cm.

Similarly, the segment MO is the middle line of the triangle BCD, MO = BC / 2 = 20/2 = 10 cm.

Answer: The length of the larger segment of the middle line is 12.5 cm.

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