Identify properties of rectangles

Detailed Explanation: Identify properties of rectangles

A rectangle is a quadrilateral with four right angles. This is the defining property, so the rectangle may be horizontal, vertical, or tilted.

Once a figure is a rectangle, these properties also follow:

• Opposite sides are parallel and equal in length.
• Adjacent sides are perpendicular.
• The diagonals are equal in length and bisect one another.

Worked example

Problem: Quadrilateral $ABCD$ is tilted on a page. Its four angles are right angles. Also,

• $AB=CD=6$ cm
• $BC=DA=4$ cm
• Diagonals $\overline{AC}$ and $\overline{BD}$ are equal and meet at each other’s midpoint.

Is $ABCD$ a rectangle? Describe its properties.

Step 1: Check the defining property.

The figure has four right angles:

Therefore, $ABCD$ is a rectangle.

Step 2: Identify its side properties.

The opposite sides are equal:

and

Opposite sides are also parallel:

Step 3: Identify its angle and diagonal properties.

Adjacent sides are perpendicular because they meet at right angles. The diagonals are equal and bisect one another, meaning they cut each other into two equal parts.

The fact that the rectangle is tilted does not change its properties. A figure is classified by its attributes, not by how it looks or how it is turned.

Remember: A square is a special rectangle because it also has four right angles. In addition, all four of its sides are equal.