Types and Properties of Quadrilaterals

Jul 11, 2024

Quadrilateral

Introduction

  • Plane Surface: A 2D flat surface extending in two directions
  • Plane Curve: A path connecting curves without lifting the pencil
  • Curves: Open and Closed Curves
  • Polygon: A closed figure made of line segments, an open curve is not a polygon
  • Examples of Polygon: Triangle (3 sides), Quadrilateral (4 sides), Pentagon (5 sides), Hexagon (6 sides)

Types of Polygons

  1. Convex Polygon:
    • Diagonals remain inside
    • Example: Square
  2. Concave Polygon:
    • Some diagonals lie outside the polygon
  3. Regular Polygon:
    • All sides and angles are equal
    • Example: Equilateral Triangle, Square
  4. Irregular Polygon:
    • Sides and angles are not equal
    • Example: Scalene Triangle, Rectangle

Sum of Exterior Angles

  • The sum of exterior angles of any polygon = 360 degrees
  • Applicable to both regular and irregular polygons

Quadrilateral

  • 4 sides, 4 angles, 4 vertices
  • Can be regular or irregular
  • Examples: Square, Parallelogram, Rectangle, Trapezium, Rhombus

Types of Quadrilaterals

  1. Trapezium

    • One pair of parallel sides

  2. Kite

    • Two pairs of adjacent sides equal
    • Diagonals are perpendicular

  3. Parallelogram

    • Both pairs of opposite sides are parallel
    • Opposite sides and angles are equal
    • Diagonals bisect each other

  4. Rhombus

    • All sides are equal
    • Includes all properties of a parallelogram

  5. Rectangle

    • Opposite sides parallel and equal
    • All angles are 90 degrees

  6. Square

    • All properties of a rectangle + all sides equal

Angle Sum Property of Quadrilateral

  • Sum of interior angles = 360 degrees
  • Applicable to all quadrilaterals

Properties of Quadrilateral

  • Parallelogram
    • Opposite sides parallel and equal
    • Opposite angles equal
    • Diagonals bisect each other
  • Rhombus
    • All sides equal
    • Diagonals intersect at 90 degrees
  • Rectangle
    • Opposite sides parallel and equal
    • All angles are 90 degrees
    • Diagonals are of equal length and bisect each other
  • Square
    • All sides equal + all angles 90 degrees
    • Diagonals are of equal length, bisect each other and are perpendicular

Conclusion

  • Review of Introduction
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