Lesson 5: Rectangles and Squares

Property

A rectangle is a parallelogram with four right angles. All angles in a rectangle are congruent and measure $90^\circ$.

Examples

• A quadrilateral with vertices at $(0, 0)$, $(5, 0)$, $(5, 3)$, and $(0, 3)$ is a rectangle.
• If a parallelogram has one right angle, it must be a rectangle because its other properties force all other angles to be $90^\circ$.
• All squares are special types of rectangles.

Explanation

A rectangle is a specific type of parallelogram, which means it inherits all the properties of a parallelogram, such as having opposite sides that are parallel and equal in length. The defining characteristic that distinguishes a rectangle from other parallelograms is that all four of its interior angles are right angles ($90^\circ$). This places rectangles as a sub-category of parallelograms within the hierarchy of quadrilaterals.

Property

A square is a quadrilateral with four right angles and four congruent sides. It is a special type of rectangle where all sides are equal in length.

Examples

• A quadrilateral with vertices at $(0, 0)$, $(4, 0)$, $(4, 4)$, and $(0, 4)$ is a square.
• A rectangle with a length of 7 cm and a width of 7 cm is a square.
• A rhombus with four right angles is a square.

Explanation

A square is defined as a quadrilateral that has four equal sides and four right angles ($90^\circ$). Because it has four right angles, every square is also a rectangle. However, not all rectangles are squares, as rectangles only need to have opposite sides be equal. A square is the most specific type of parallelogram, as it is both a rectangle and a rhombus.