Lesson 5 — Trapezoids

Big idea: A trapezoid has exactly one pair of parallel sides; an isosceles trapezoid has equal legs and equal base angles.

Words to know

Word	Meaning
Trapezoid	A quadrilateral with exactly one pair of parallel sides.
Bases	The parallel sides of a trapezoid.
Legs	The nonparallel sides of a trapezoid.
Base angles	The pairs of angles that include each base.
Isosceles trapezoid	A trapezoid whose legs are equal.

Theorem 35: The base angles of an isosceles trapezoid are equal.

Theorem 36: The diagonals of an isosceles trapezoid are equal.

The bases are parallel; the legs are not.
In an isosceles trapezoid:
- legs are equal;
- base angles are equal (one pair at each base);
- diagonals are equal.
A trapezoid is not a parallelogram, because it has exactly one pair of parallel sides.

If the homework asks…	Do this…
Find a missing angle	Use the equal base angles and the 360° sum.
Prove a trapezoid is isosceles	Show the legs are equal, or show base angles are equal.
Use diagonals	In an isosceles trapezoid, the diagonals are equal.
Classify a quadrilateral	Count pairs of parallel sides: 1 pair = trapezoid; 2 pairs = parallelogram.
Set up algebra	Set equal base angles equal; use the angle sum 360°.

An isosceles trapezoid has a base angle of 70°.

The other angle at the same base is also 70°. The angles at the other base are:

180° − 70° = 110° each

So the angles are 70°, 70°, 110°, 110°.

A trapezoid has exactly one pair of parallel sides.
The equal base angles are the two angles at the same base, not one from each base.
The diagonals of an isosceles trapezoid are equal, but not necessarily perpendicular.
Do not confuse a trapezoid with a parallelogram.