Compute the coordinates of M and N:
M = (A + B)/2 = (b, c).N = (C + D)/2 = (a + d, c)
y-coordinates of M and N equal (c), so MN is parallel to AD. The same can be said about BC (B and C have the same y-coordinates).So we proved 1.
For 2, lets compute the lengths:
AD = 2a, BC = 2d - 2b, MN = a+d - b.So (AD + BC)/2 = a+d-b = MN, QED.
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