Identify properties of rectangles

Detailed Explanation: Identify properties of rectangles

A rectangle is a four-sided shape with these properties:

• It has four right angles.
• Its opposite sides are parallel.
• Its opposite sides are equal in length.
• Neighboring sides do not have to be equal.

A rectangle can be turned or stretched in a drawing and still be a rectangle. A square is also a rectangle because it has four right angles and matching opposite sides. A square has the extra property that all four sides are equal.

Example: Is quadrilateral $ABCD$ a rectangle?

Suppose the diagram shows that:

• $\angle A$, $\angle B$, $\angle C$, and $\angle D$ are all right angles.
• $AB=8$ cm and $CD=8$ cm.
• $BC=5$ cm and $AD=5$ cm.
• $AB$ is parallel to $CD$, and $BC$ is parallel to $AD$.

Step 1: Count the sides.
$ABCD$ has four sides, so it is a quadrilateral.

Step 2: Check the angles.
All four angles are right angles. This is the most important property of a rectangle.

Step 3: Check opposite sides.
The opposite sides match:

and

The opposite sides are also parallel.

Step 4: Decide.
Because the shape has four sides, four right angles, and equal, parallel opposite sides, $ABCD$ is a rectangle.

The sides next to each other have different lengths, $8$ cm and $5$ cm, but that is allowed. They do not need to be equal.