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Summary

  • A curve is a set of connected points.
  • A simple curve is a curve that does not intersect itself at any point other than possibly at the endpoints.
  • A closed curve is a curve that begins and ends at the same point.
  • A polygon is a simple closed curve composed of a finite number of line segments.
  • The line segment joining two vertices of a polygon is called an edge or side.
  • A polygon in which all sides are equal and all angles are equal is called regular polygon.
  • Polygons which are not regular are called irregular polygons. That is, their sides and angles are not equal.
  • A polygon is said to be concave if all its diagonals lie inside the polygon.
  • A polygon is said to be convex if at least one of the diagonal lies outside it.
  • Sum of interior angles of a polygon = Number of triangles in the polygon ´ 180°
  • Sum of exterior angles of a polygon is 360°. 
  • A quadrilateral in which one pair of opposite sides is parallel is called a trapezium.
  • A quadrilateral in which both pairs of opposite sides are equal is called a parallelogram. 
  • A parallelogram in which all angles are right angles is called a rectangle.
  • A parallelogram in which all sides are equal is called a rhombus.
  • A rectangle in which all sides are equal is called a square.
  • In a parallelogram
    • opposite sides are parallel 
    • opposite sides are equal 
    • opposite angles are equal 
    • diagonals bisect each other 
  • In a rectangle the diagonals are equal and they bisect each other
  • In a rhombus diagonals bisect each other at right angles 
  • In a square diagonals are equal and they bisect each other at right angles.




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