For trapezoid QRST, A and B are midpoints of the legs. Find AB, m<Q, and m<S.
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1. Find AB
Definition of mid-segment of trapezoid:
A segment whose endpoints are the midpoints of the nonparallel sides (of the trapezoid).
If b is the measure of the upper base of the trapezoid and d is the measure of the lower base of the trapezoid, then the measure of the mid-segment of the trapezoid is $\displaystyle \frac{b+d}{2}$
2. Find m<Q, and m<S.
The trapezoid has 2 (or 3 in this case) parallel lines. Remember that:
If two parallel lines are cut by a transversal, then:
- Alternate interior angles are congruent
- Corresponding angles are congruent
- Same side interior angles are supplementary