Lecture Notes: Special Types of Quadrilaterals

Introduction to Quadrilaterals

• Quadrilateral: A four-sided polygon.

Types of Quadrilaterals

Square

• Definition: Four congruent sides and four right angles (90° each).
• Area: (s \times s = s^2)
• Perimeter: (4s)
• Example: Given area 36 square inches, side length = 6 inches, perimeter = 24 inches.

Rectangle

• Properties:
  • Four right angles.
  • Opposite sides are congruent.
• Area: Length ( \times ) Width
• Perimeter: (2L + 2W)
• Diagonal: Use Pythagorean theorem: (c^2 = a^2 + b^2)
• Example: Width = 5, Length = 12, Area = 60 square units, Perimeter = 34 units, Diagonal = 13 units.

Rhombus

• Properties:
  • Four congruent sides.
  • Opposite angles are congruent; consecutive angles are supplementary.
• Area: (\frac{1}{2} \times D1 \times D2)
• Perimeter: 4 ( \times ) side length
• Example: Diagonals 12 and 16, Area = 96 square units, Perimeter = 40 units.
• Diagonals:
  • Form right angles and bisect opposite angles.

Kite

• Properties:
  • Two pairs of adjacent congruent sides.
  • Diagonals are perpendicular.
  • One diagonal bisects the other.
• Area: (\frac{1}{2} \times D1 \times D2)
• Perimeter: Sum of all sides, calculated using Pythagorean theorem.
• Example: Diagonals parts 12, 16, Area = 252 square units, Perimeter = 66 units.
• Angles: One pair of opposite angles is congruent.

Parallelogram

• Properties:
  • Opposite sides are parallel and congruent.
  • Opposite angles are congruent; consecutive angles are supplementary.
• Area: Base ( \times ) Height
• Example: Base = 10, Height = 8, Area = 80 square units.

Trapezoid

• Properties:
  • One pair of parallel sides.
• Area: (\frac{1}{2} \times (B1 + B2) \times \text{Height})
• Example: Bases 10 and 20, Height = 12, Area = 180 square units.
• Isosceles Trapezoid:
  • Non-parallel sides are congruent.
  • Base angles are congruent.

Conclusion

• Overview of special quadrilaterals and their properties.