Trapezoids - Interactive Activity

A trapezoid is a quadrilateral with exactly one pair of parallel sides. These activities let you drag a trapezoid into new shapes and watch its properties stay true, name the property a picture shows, and build complete solutions one step at a time.

Definitions and Main Ideas

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.

The Polygon Family Tree

Properties are inherited as we move down the tree. The highlighted shapes, Trapezoid and Isosceles Trapezoid, are the shapes in this lesson.

Trapezoid Explorer

What to do: Drag the orange handle at B to change the top base, the purple handle at D to move the bottom base line, or the dark cyan handle at C to change the bottom base. The two bases stay parallel, so the figure is always a trapezoid. Watch the readouts as you drag.

A move that would make the two bases equal, make the legs parallel, make two measures look equal when they are not, push the figure off the drawing area, or flatten an angle too far is not accepted.

Name the Property

What to do: Look at the highlighted parts of the trapezoid and at the values shown. Choose the property the picture shows. A first miss gives a hint and another try. The Next problem button cycles through all eight problems in order.

The Next problem button cycles through all eight problems in order.

Build the Solution

What to do: Work each problem one step at a time. Step 1 chooses the equation that should be used to solve the problem. A first miss gives a hint and another try. The gold highlight marks the part the current step asks about, and a part solved in an earlier step is labeled with its found value.

Continue moves to the next step. New problem cycles through all six problems in order.

Your Turn

What to do: Answer all six questions. A first miss gives a hint and another try; after a second miss the answer is shown and explained. Your score counts first-try answers only.

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Trapezoids — Mr. J Geometry. All activities on this page run entirely in your browser.