Textbook Problem

Use Exercise 33 and the following drawing to complete the proof of this theorem: “The length of the median of a trapezoid is one-half the sum of the lengths of the two bases”.

Given:	Trapezoid $ABCD$ with median $\overline{MN}$
Prove:	$MN=\frac{1}{2}(AB+CD)$

33. Use Theorem $\mathrm{5.6.1}$ and the drawing to complete the proof of this theorem: “If a line is parallel to one side of a triangle and passes through the midpoint of a second side, then it will pass through the midpoint of the third side.”

Given:	$\Delta RST$ with $M$ the midpoint of $\overline{RS;}\stackrel{\leftrightarrow }{MN}\parallel \overline{ST}$
Prove:	$N$ is the midpoint of $\overline{RT}$