Quadrilateral

Introduction

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

Types of Polygons

1. Convex Polygon:

   • Diagonals lie inside
   • Example: Square

2. Concave Polygon:

   • Some diagonals lie outside the polygon

3. Regular Polygon:

   • All sides and angles are equal
   • Examples: Equilateral Triangle, Square

4. Irregular Polygon:

   • Sides and angles are not equal
   • Examples: Scalene Triangle, Rectangle

Sum of Exterior Angles

• Sum of exterior angles of any polygon = 360 degrees
• Applies 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 are 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 are parallel and equal
   • All angles are 90 degrees

6. Square

   • Includes all properties of a rectangle + all sides are equal

Angle Sum Property of Quadrilateral

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

Properties of Quadrilaterals

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

Conclusion

• Review of the introduction
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