In the trapezoid ABCD MN is the middle line BC, AD of the base BC = 4 AC = 10 BD is the diagonal of the trapezoid Find the lengths of the segments into which the diagonal divides the middle line of the trapezoid.
Since MN is the middle line of the trapezoid, it bisects the sides of the trapezoid, AM = BM, DN = CN and is parallel to its bases.
Then in the BCD triangle the segment NK is its middle line, then NK = BC / 2 = 4/2 = 2 cm.
In the ABD triangle, the MK segment is its middle line, then MK = AD / 2 = 10/2 = 5 cm.
Answer: Diagonal BD divides the middle line into 2 cm and 5 cm segments.
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