I'm not sure about this. How do I PROVE the midline theorem? What is the diagonal supposed to indicate? A clear explanation could really help. Thank you!

Question

536.If M and N are the midpoints of the non-parallel sides of a trapezoid, it makes sense to call the segment MN the mid- line of the trapezoid. Why? (It actually should be called the midsegment, of course. Strange to say, some textbooks call it the median). Suppose that the parallel sides of a trapezoid have lengths 7 and 15. What is the length of the midline of the trape- zoid? Notice that the midline is divided into two pieces by a diagonal of the trapezoid. What are the lengths of these pieces? Does it matter which diagonal is drawn?

Answer 1

First, it is easy to show that MN is parallel to the parallel sides of the trapezoid.

Then if you drop perpendiculars from the ends of the of the small base to the larger base, you can use similar triangles to show that the length of MN is 11.

Each diagonal divides MN into 2 segments and the diagonal is bisected by MN

Without the height of the trapezoid I think you do not have enough information to calculate the length of the diagonal.