The diagram at right shows a midsegment of a trapezoid. That is, $\overline{EF}$ is a midsegment because points $E$ and $F$ are both midpoints of the non-base sides of trapezoid $ABCD$.

1. If $A(0, 0)$, $B(9, 0)$, $C(5, 6)$, and $D(2, 6)$, find the coordinates of points $E$ and $F$. Then compare the lengths of the bases ($\overline{AB}$ and $\overline{CD}$) with the length of the midsegment $\overline{EF}$. What is the relationship among the segments?

   Hint (a):

   How do you find the lengths from coordinates?
   Think of how the answers could be related.

   Answer (a):

   It seems to be the average of $AB$ and $CD$.

2. Verify that the relationship you observed in part (a) holds if $A(–4, 0)$, $B(2, 0)$, $C(0, 2)$, and $D(–2, 2)$.

   Hint (b):

   Use the same method you used to solve part (a).

3. Write a conjecture about the midsegment of a trapezoid.

   Answer (c):

   The midsegment of a trapezoid is parallel to the bases and has a length that is the average of the lengths of the bases.