Class 8 Chapter 12: Understanding Quadrilaterals

# Class 8 Chapter 12: Understanding Quadrilaterals

Important Concepts and Formulas

1.      A simple curve is a curve that does not cross itself at any point.

2.      A curve is said to be closed if it begins and ends at the same point.

3.      A polygon is a closed figure made up of three or more line segments.

4.      In a polygon, if the line joining any two points on it lies inside the polygon, then the polygon is a convex polygon.

5.      In a polygon, if there is even one diagonal which does not lie inside it completely, then the polygon is called concave polygon.

6.      The polygon in which all the sides and all the angles are equal is called a regular polygon.

8.      The sum of the exterior angles of a convex polygon is 360°.

9.      A rectilinear closed figure with four sides is called a quadrilateral.

10. The examples of quadrilaterals are parallelogram, rhombus, rectangle, square, trapezium and kite.

11. A parallelogram is a quadrilateral with each pair of opposite sides being parallel, such that
·        opposite sides are equal,
·        opposite angles are equal, and
·        diagonals bisect each other.

12. A rhombus is a parallelogram with all sides of equal length and
·        holding all properties of a parallelogram,
·        diagonals are perpendicular to each other.

13. A rectangle is a parallelogram with all right angles and
·        holding all properties of a parallelogram,
·        diagonals are equal.

14. A square is a rectangle with all sides of equal length and holding all properties of a parallelogram, a rhombus and a rectangle.

15. A trapezium is a quadrilateral with one pair of opposite sides parallel.

16. A kite is a quadrilateral with exactly two pairs of equal adjacent sides and
·        the diagonals are perpendicular to each other.
·        one of the diagonals bisects the other.

17. The relation between the number of sides (n) of a polygon and the number of diagonals (D) is D = ½ × n(n – 3).