Question

Prove: The segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases.

Answer 1

M(b/2 ,c/2 )
Midpoint of BD=((a+d)/2 ,c /2 )
slope of AB = 0
Slope of MN =((c/2-c/2)/ ((a+d)/2-c/2 ))=0

Answer 2

M = (d/2, c/2)

N = (a+b/2, c/2)

MN = a+b-d/2

AB = a

CD = b - d

MN = 1/2 (a + b - d)