# 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

September 12, 2021 | education

| **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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