# In isosceles trapezoid ABCD, the points M and N are the midpoints of the diagonals AC and BD

In isosceles trapezoid ABCD, the points M and N are the midpoints of the diagonals AC and BD, respectively. Find the length of the segment MN if BC = 10, AD = 16.

Since points M and N are the midpoints of the trapezoid diagonals, the segment MN lies on the midline of the trapezoid. Let’s draw the middle line of the CD. Then, in the ВСD triangle, the segment NP is its midline, then NP = BC / 2 = 10/2 = 5 cm.

The KM segment is the middle line of the ABC triangle, then KM = BC / 2 = 10/2 = 5 cm.

Determine the length of the midline of the trapezoid.

KР = (BC + AD) / 2 = (10 + 16) / 2 = 13 cm.

Then the segment MN = KP – KM – NP = 13 – 5 – 5 = 3 cm.

Answer: The length of the segment MN is 3 cm.

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