Hello students, in this blog you can learn about polygons, types of quadrilaterals, their important properties and formulas. This can be used to solve problems from this chapter and also for important entrance/ competitive exams and Olympiads.

#### 1. **Polygon** : A polygon is a simple closed curve made up of only line segments.

#### 2. **Diagonal of a polygon** : It is a line segment connecting two non-consecutive vertices of the polygon.

#### 3. Number of diagonals in a polygon of n sides :

#### 4. **Convex polygon** : It is a polygon in which all its interior angles less than 180◦.

#### 5. **Quadrilateral** : It is a polygon having only four sides.

#### 6. **Regular polygon** : It is a polygon whose all sides are equal and also all angles are equal.

#### 7. Sum of interior angles of a polygon of n sides : **(n − 2)×180◦** .

#### 8. Sum of interior angles of a quadrilateral = **360◦** .

#### 9. Sum of exterior angles of a polygon a

(taken in order) = **360**◦ .

#### 10. **Trapezium** : a quadrilateral in which a pair of opposite sides is parallel.

#### 11. **Kite** : a quadrilateral which has two pairs of equal consecutive sides.

#### 12. **Parallelogram** : a quadrilateral in which each pair of opposite sides is parallel.

• opposite a sides are equal,

• opposite angles are equal.

• diagonals bisect each other

#### 13. **Rhombus** : a parallelogram in which adjacent sides are equal.

• diagonals intersect at right angles

#### 14. **Rectangle** : a parallelogram in which one angle is of 90◦ .

• diagonals are equal

#### 15. **Square** : a parallelogram in which adjacent sides are equal and one angle is of 90◦.

#### 16. **A unique quadrilateral** can be determined by: five measurements

• if the lengths of its four sides and a diagonal are given

• if the lengths of its three sides and two diagonals are given.

• if its two adjacent sides and three angles are given

• if its three sides and two included angles are given.

Based on the above summary notes, take a test. To download the test paper with answers:

*************************