Identify properties of trapezoids

Detailed Explanation: Identify properties of trapezoids

A trapezoid is a quadrilateral with at least one pair of parallel sides.

• The parallel sides are called the bases.
• The other two sides are called the legs.
• The trapezoid can be turned or tilted; its position does not matter.
• The legs or base angles do not have to be equal. If the legs are equal, it is the special type called an isosceles trapezoid.

Worked example

Look at quadrilateral $ABCD$. The diagram marks $AB$ and $CD$ with matching arrows, showing that

The side lengths are:

Step 1: Find the parallel sides.

The matching arrows tell us that $\overline{AB}$ and $\overline{CD}$ are parallel.

Step 2: Name the bases.

The parallel sides are the bases:

• $\overline{AB}$ is one base.
• $\overline{CD}$ is the other base.

Step 3: Name the legs.

The remaining sides are the legs:

• $\overline{BC}$ is one leg.
• $\overline{DA}$ is the other leg.

Step 4: Decide whether it is an isosceles trapezoid.

The legs have lengths $6$ and $4$, so they are not equal:

Therefore, this is a trapezoid, but it is not an isosceles trapezoid.

Always look for parallel sides rather than judging by how the shape looks.