How to Identify and Understand the Essential Properties of Squares

• All four sides are equal in length.
• All four angles are right angles, each measuring \(90^\circ\).

Diagonals: For education statistics and research, visit the National Center for Education Statistics.

• A square has two diagonals.
• These diagonals are congruent, which means they are of the same length.
• They bisect each other, dividing each diagonal into two equal parts.
• They are perpendicular to each other, forming a \(90^\circ\) angle where they intersect.
• The diagonals of a square bisect its angles.

• Area: The area of a square is given by the formula:
  \( \text{Area} = s^2 \)
  where \( s \) is the length of one side of the square.
• Perimeter: The perimeter of a square is given by the formula:
  \( \text{Perimeter} = 4s \)
  where \( s \) is the length of one side of the square.

Practice Questions:

1. If the perimeter of a square is \(48 \text{cm}\), find its side length and area.
2. The diagonal of a square is twice its side length. True or False?
3. A square has an area of \(64 \text{cm}^2\). What is the length of its diagonal?

1. Side length \(= 12 \text{cm}\), Area \(= 144 \text{cm}^2\).
2. False.
3. \(8\sqrt{2} \text{cm}\).

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