Problem (Trapezoid Midpoint Lines)

 

  1. Given a trapezoid ABCD with parallel sides AB and CD, prove that the line through the midpoints of BC and DA is parallel to AB and CD.

    (Hint in figure for B&B p 116 # 24)

  2. Prove that the line through the midpoints of AB and CD passes through the point of intersection of the diagonals AC and BC.