A middle line is drawn in a trapezoid with bases 6 and 2. Find the length of its segment enclosed

univerkov | June 15, 2021 | education

A middle line is drawn in a trapezoid with bases 6 and 2. Find the length of its segment enclosed between the diagonals of the trapezoid.

Determine the length of the midline of the trapezoid ABCD.

KM = (BC + AD) / 2 = (2 + 6) / 2 = 4 cm.

In triangle ABC, segment KH is its midline, since point K is the midpoint of side AB, and point H is the midpoint of the diagonal AC, since it is intersected by the midline of the trapezoid.

Then KH = BC / 2 = 2/2 = 1 cm.

Similarly, in a triangle ВСD, the segment МР is its middle line, then МР = ВС / 2 = 2/2 = 1 cm.

Then the required segment НР = КМ – КН – МР = 4 – 1 – 1 = 2 cm.

Answer: The length of the segment between the diagonals is 2 cm.

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