Trapezoids
Overview
A trapezoid sits on its own branch of the family tree: it has exactly one pair of parallel sides, called the bases, while a parallelogram has two. The angles along each leg are supplementary, and the midsegment (median) of a trapezoid is parallel to the bases with a length equal to half the sum of the bases. An isosceles trapezoid adds congruent legs, congruent base angles, and congruent diagonals.
Vocabulary
- Trapezoid
- A quadrilateral with exactly one pair of parallel sides. The bases of a trapezoid are never congruent.
- Bases
- The two parallel sides of a trapezoid.
- Legs
- The two non-parallel sides of a trapezoid.
- Base Angles
- A pair of angles that share a base of a trapezoid. A trapezoid has two pairs of base angles, one pair at each base.
- Median (Midsegment) of a Trapezoid
- The segment that connects the midpoints of the legs. It is parallel to the bases, and its length is half the sum of the lengths of the bases.
- Isosceles Trapezoid
- A trapezoid whose legs are congruent. In an isosceles trapezoid, each pair of base angles is congruent and the diagonals are congruent.
Main Ideas
- A trapezoid has exactly one pair of parallel sides; a parallelogram, with two pairs, is not a trapezoid.
- The angles along one leg, between the bases, are consecutive interior angles for the parallel bases, so they are supplementary.
- The median (midsegment) of a trapezoid is parallel to both bases.
- Median length = ½(b₁ + b₂): the median is the average of the two bases.
- In an isosceles trapezoid the legs are congruent, each pair of base angles is congruent, and the diagonals are congruent.
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Practice Problems
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