In the trapezoid abcd with bases ad = 32 cm and bc = 18 cm, the middle line pq is drawn, which intersects

In the trapezoid abcd with bases ad = 32 cm and bc = 18 cm, the middle line pq is drawn, which intersects the diagonals ac and bd at points m and n. Determine the value of the segment mn.

Determine the length of the midline PQ of the trapezoid ABCD.

PQ = (AD + BC) / 2 = (32 + 18) / 2 = 25 cm.

Consider a triangle ABC. Point P is the middle of AB, then PM is the middle line of triangle ABC. Since the midline of a triangle is half the length of the side of the triangle parallel to the midline, PM = BC / 2 = 18/2 = 9 cm.

Similarly, consider the triangle BСD, which has NQ as its middle line. NQ = BC / 2 = 18/2 = 9 cm.

Then the segment MN = PQ – PM – NQ = 25 – 9 – 9 = 7 cm.

Answer: MN = 7 cm.