Properties of Squares and Rectangles

Definition: 

A rectangle is a quadrilateral with four right (90°) angles. They are parallelograms with the following properties:
– Both pairs of opposite sides are congruent
– Diagonals are congruent and bisect each other
– Four right angles

A square is a quadrilateral with four right angles and all sides congruent. All squares are rectangles, rhombi, parallelograms and have the following properties:
– Diagonals are congruent, perpendicular, and bisect both each other and the interior angles
– All sides are congruent
– Four right angles

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Example: List the similarities and differences between squares and rectangles.

Solution:

Step 1: Observe the similarities between squares and rectangles:

Both are quadrilaterals and parallelograms, because they have four sides with parallel opposite sides. Both have four right angles. Both have congruent diagonals that bisect each other

Step 2: Observe the differences between squares and rectangles:

Rectangles have two pairs of congruent opposite sides, while squares have four congruent sides. Only squares have perpendicular diagonals that bisect the interior angles

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