**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.

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°.

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).