Question

ABCD is a trapezoid with median MN. If DC=6 and AB=16, find ME, FN, and EF.​

Answer 1

• ME = 3
• FN = 3
• EF = 5

Explanation:

You want the lengths of the three segments of trapezoid midline MN formed by the diagonals when the trapezoid bases are 6 and 16.

Triangle midlines

Midline MN is halfway between the parallel bases CD and AB, so is the average of their lengths:

MN = (CD +AB)/2 = (6 +16)/2 = 11

That MN is a midline means segments ME and FN are midlines of their respective triangles, ACD and BCD, so half the length of base CD:

ME = FN = 6/2 = 3

Segment EF

The remaining segment (EF) of MN is of length can be found from the sum of the line segments.

ME +EF +FN = MN

3 +EF +3 = 11 . . . . . . use known lengths

EF = 5 . . . . . . . . . subtract 6