Points M and N of the middle of the diagonals of the trapezoid ABCD find the length of the segment MN

Points M and N of the middle of the diagonals of the trapezoid ABCD find the length of the segment MN if the base of the trapezoid AD and BC are equal to 10 and 4, respectively.

Let’s draw the middle line KP of the trapezoid ABCD.

Points M and N will lie on the middle line of the trapezoid, since they are the midpoints of its diagonals.

Determine the length of the midline of the trapezoid.

КP = (ВС + АD) / 2 = (4 + 10) / 2 = 14/2 = 7 cm.

In the ABC triangle, the KM segment is its middle line, since KM is parallel to BC, and AK = BK and AM = CM.

Then KM = BC / 2 = 4/2 = 2 cm.

Similarly, in the DVS triangle, the segment РN = ВС / 2 = 4/2 = 2 cm.

Then MN = KP – KM – PN = 7 – 2 – 2 = 3 cm.

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