Quadrilaterals

• A quadrilateral is a polygon having four sides four angles and four vertices.
• The word “quadrilateral” is derived from the Latin words “quadri,” which means four, and “latus”, which means sides.
• Quadrilaterals are named using consecutive vertices.
• The symbol □ is used to denote a quadrilateral
• Parallelogram - two pairs of parallel sides.
• Rectangle - four right angles
• Rhombus - two pairs of congruent sides
• Square - four congruent angles, four congruent sides.
• Trapezoid - exactly one pair of parallel sides
• Kite - two pairs of congruent sides, its opposite sides are not congruent.
• Two parallel lines - Trapezoid

  Two pairs of parallel lines - Parallelogram: Rhombus, Rectangle, Square

  No parallel sides - Kite
• Quadrilateral Angle-Sum Theorem

  • Exterior Angles of a Quadrilateral - An exterior angle is formed by the intersection of any of the sides of a polygon and extension of the adjacent side. The sum of all the exterior angles of a quadrilateral is 360°.
• Rectangles, Squares, and Rhombuses are also parallelograms.
• Quadrilaterals can be classified into

  • Parallelograms
  • Rectangles
  • Rhombuses
  • Squares
  • Trapezoids
  • Kites
• Some properties are common to all quadrilaterals. These properties are:

  • They have four vertices.
  • They have four sides.
  • The sum of all interior angles is 360°.
  • They have two diagonals.
• • A quadrilateral can be regular or irregular.
  • A regular quadrilateral must have four equal sides, and four equal angles, and its diagonals must bisect each other.
  • Square is the only regular quadrilateral