- What is Closed curve and Open curve
- |
- What are polygons
- |
- Classification of polygons
- |
- Convex and Concave Polygons
- |
- Regular and Irregular Polygons
- |
- Angle Sum in the Polygons
- |
- What is Quadrilaterals
- |
- Types of Quadrilaterals

Open curve is a figure in the place with end points

We classify polygons according to the number of sides( or vertices)

Number of sides |
Classification |

3 |
Triangle |

4 |
Quadrilateral |

5 |
Pentagon |

6 |
Hexagon |

7 |
Heptagon |

8 |
Octagon |

9 |
Nonagon |

We have all the diagonals inside the Polygon

We don’t have all the diagonals inside the Polygon

We will be concentrating on Convex Polygon in this chapter

So all the sides and angles should be same

a) So square is a regular polygon but rectangle is not

b) Equilateral triangle is a regular polygon

=(n-2) × 180

For Triangle, n=3

So Total =180

For quadrilateral, n=4

So total =360

Find the value of angle x

We know in the quadrilateral, sum of interior angle is 360

So

50+130+120+x=360

x=60

This property is very useful is finding number of sides of the polygons

Find the number of sides of a regular polygon whose each exterior angle

has a measure of 60°.

Measure of each exterior angle = 60°

Therefore, the number of exterior angles =360/60=6

The polygon has 6 sides.

Sum of angles of the Quadrilaterals =360

Sum of exterior angles of the Quadrilaterals =360

Trapezium is a quadrilateral with a pair of parallel sides.

Trapezium when non-parallel sides of it are of equal length

It is a quadrilaterals having exactly two distinct consecutive pairs of sides of equal length

Here ABCD is a Kite

AB=BC

AD=CD

It is a quadrilateral whose opposite sides are parallel.

Here ABCD is a Parallelogram

AD || BC, AB ||CD

The opposite sides of a parallelogram are of equal length.

AD=BC , AB=CD

The opposite angles of a parallelogram are of equal measure

∠A= ∠C , ∠B= ∠D

The adjacent angles in a parallelogram are supplementary.

∠A+ ∠D=180 , ∠B+ ∠C=180

The diagonals of a parallelogram bisect each other

Find the value of the angles x,y,z in the parallelograms given above

Angle B and Angle D are opposite angle and are equal

So y=100

Angle C and Angle B are adjacent angle and are supplementary

So x+100=180

x=80

Angle A and Angle C are opposite angle and are equal

So z=80

A rhombus is a quadrilateral with sides of equal length

A rhombus has all the properties of a parallelogram and also that of a kite.

The diagonals of a rhombus are perpendicular bisectors of one another

A rectangle is a parallelogram with equal angles

Each angle is of 90

The diagonals of a rectangle are of equal length

A square is a rectangle with equal sides.

So it has the same property of Rectangle in addition of 4 equal sides

The diagonals of a square are perpendicular bisectors of each other.

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