Quadrilaterals: Rectangles and Squares

Quadrilaterals

Rectangles

• A rectangle is a quadrilateral with four right angles (90°)
• All sides are not equal in length
• Opposite sides are equal in length
• Diagonals are equal in length
• Can be a square if all sides are equal

Squares

• A square is a rectangle with all sides of equal length
• All internal angles are right angles (90°)
• All sides are equal in length
• Diagonals are equal in length and bisect each other at 90°
• A square is a special type of rectangle and rhombus

Trapezoids

• A trapezoid is a quadrilateral with two pairs of opposite sides
• One pair of opposite sides is parallel (called bases)
• The other pair of opposite sides is not parallel (called legs)
• Can be classified as:
  • Isosceles trapezoid: legs of equal length
  • Scalene trapezoid: all sides of different lengths

Kites

• A kite is a quadrilateral with two pairs of adjacent sides of equal length
• One pair of opposite angles is equal
• The diagonals are perpendicular and one diagonal bisects the other
• Can be classified as:
  • Rhombus kite: all sides of equal length
  • Non-rhombus kite: not all sides of equal length

Rhombi

• A rhombus is a quadrilateral with all sides of equal length
• Opposite sides are parallel and opposite angles are equal
• Diagonals are perpendicular and bisect each other at 90°
• Can be a square if all internal angles are right angles (90°)

Quadrilaterals

Rectangles

• Have four right angles (90°)
• Opposite sides are equal in length
• Diagonals are equal in length
• Can be a square if all sides are equal

Squares

• Are rectangles with all sides of equal length
• Have all internal angles of 90°
• All sides are equal in length
• Diagonals are equal in length and bisect each other at 90°
• Are a special type of rectangle and rhombus

Trapezoids

• Have two pairs of opposite sides
• One pair of opposite sides is parallel (bases)
• The other pair of opposite sides is not parallel (legs)
• Can be isosceles (legs of equal length) or scalene (all sides of different lengths)

Kites

• Have two pairs of adjacent sides of equal length
• One pair of opposite angles is equal
• Diagonals are perpendicular and one diagonal bisects the other
• Can be a rhombus kite (all sides of equal length) or non-rhombus kite (not all sides of equal length)

Rhombi

• Have all sides of equal length
• Opposite sides are parallel
• Opposite angles are equal
• Diagonals are perpendicular and bisect each other at 90°
• Can be a square if all internal angles are 90°