2.10: Properties of Rectangles and Squares
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 \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.
Reading Check:
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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