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2.10: Properties of Rectangles and Squares

Difficulty Level: At Grade Created by: CK-12

Learning Objectives

• Identify and classify a rectangle.
• Identify and classify a square.
• Identify the relationship between the diagonals in a rectangle.

Rectangles and Squares

Now that you have a much better understanding of parallelograms, you can begin to look more carefully into certain types of parallelograms. This lesson explores two very important types of parallelograms—rectangles and squares.

Rectangles

A rectangle is equiangular:

• Each angle in a rectangle has the same measure.
• Each angle in a rectangle measures 90\begin{align*}90^\circ\end{align*}
• In other words, a rectangle has four right angles.
• A square is a special kind of rectangle and shares all of the properties of rectangles.

Rectangles have four ___________________________ angles.

A square is a rectangle with ________________________________ sides.

Diagonals in a Rectangle

Remember that all of the rules that apply to parallelograms still apply to rectangles and squares.

There is one additional property that is specific to rectangles:

The diagonals of a rectangle are congruent.

Do you remember the properties of parallelograms?

These apply to all parallelograms, including rectangles and squares:

• opposite sides are parallel
• opposite sides are congruent
• opposite angles are congruent
• consecutive angles are supplementary
• diagonals bisect each other

The diagonals in a rectangle and a square are _______________________________.

In a parallelogram, opposite sides are ____________________ and ___________________.

Theorem for Rectangle Diagonals

The diagonals of a rectangle are congruent.

1. True or False: All the angles in a rectangle are congruent.

2. True or False: The diagonals in a rectangle bisect each other.

3. True or False: The diagonals in a rectangle are congruent, but the diagonals in a square are not congruent.

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