Identify properties of squares

Detailed Explanation: Identify properties of squares

A square is a quadrilateral with:

• Four congruent sides: all sides have the same length.
• Four right angles: each angle measures $90^\circ$.
• Opposite sides parallel: each pair of opposite sides runs in the same direction.
• Diagonals with special properties: the diagonals are equal in length, cross at their midpoints, meet at right angles, and split the angles in half.

Because of these properties, every square is both a rectangle and a rhombus.

Example: Quadrilateral $ABCD$ has four sides of length $6$ cm and four right angles. What type of quadrilateral is it, and what are some of its properties?

Step 1: Check the sides.
All four sides measure $6$ cm, so the sides are congruent.

Step 2: Check the angles.
All four angles are right angles, each measuring $90^\circ$.

Step 3: Classify the quadrilateral.
A quadrilateral with four congruent sides and four right angles is a square. It is also a rectangle because it has four right angles, and it is a rhombus because it has four congruent sides.

Step 4: Identify more properties.
Since $ABCD$ is a square:

• $AB \parallel CD$
• $BC \parallel AD$
• Its diagonals are congruent.
• Its diagonals bisect each other.
• Its diagonals are perpendicular.
• Its diagonals bisect the angles.

If you also needed the perimeter, add the four equal sides:

So, $ABCD$ is a square with opposite sides parallel and diagonals that are equal, perpendicular, and bisect one another.