Any closed polygon having 4 sides, 4 angles and 4 vertices is called the Quadrilateral. A quadrilateral could either be a regular or an irregular polygon. The Angle sum property of a Quadrilateral is dependent on the sum of the exterior and the interior angles. It says that the sum of all the exterior angles of a Quadrilateral equals 360°. Even the sum of all the interior angles of a Quadrilateral is equal to 360°.

For understanding quadrilaterals class 8, learn about these geometrical figures for a thorough knowledge.

1. ### Plane Surface

A surface that’s completely flat like a chequered board or a paper is a plane surface.

1. ### Plane Curve

When we obtain a curve by connecting the number of certain points without picking the pencil up is a plane curve. A plane curve can be classified into 2 i.e. an open or closed curve.

Open Curve

Closed Curve

1. ### Polygons

The simple closed curves which are solely composed of line segments are called the Polygons.

Polygons are further classified by the number of sides or vertices they have. Take a look at the chart to understand all types of polygons

 Number of Sides Type of Polygon Geometrical Figure 3 Triangle (Image to be added soon) 4 Quadrilateral (Image to be added soon) 5 Pentagon (Image to be added soon) 6 Hexagon (Image to be added soon) 7 Heptagon (Image to be added soon) 8 Octagon (Image to be added soon) 9 Nonagon (Image to be added soon) 10 Decagon (Image to be added soon) n n-gon (Image to be added soon)

### Understanding Quadrilaterals Class 8 Exercise 3.2

Classify each of the following figures on the basis of the given:-

(i) Polygon

(ii) Convex polygon

(iii) Concave polygon

(iv) Simple Curve

(v) Simple Closed Curve

Lets unlock the answers to above;-

(i) 1, 2

(ii) 2

(iii) 1

(iv) 1,2,5,6,7

(v) 1,2,5,6,7

### Concave Polygon

The concave polygons are the type of polygons that have some of its diagonals in the exterior of the object.

### Convex Polygon

The convex polygons are the type of polygons that have all of its diagonals in the interior of the object.

### Regular and Irregular Polygons

Polygons that are equilateral as well as equiangular are known as Regular Polygons. In other words, a polygon is regular if-

• It’s all (four) sides are equal.

• It’s all (four) angles are equal.

Therefore, we can conclude that a square is a regular polygon but a rectangle is not since all of its sides are not equal, though the angles are equal.

### Angle Sum Property of a Polygon

The sum total of all the interior angles of a polygon stays the same as per the number of sides irrespective of the shape of the polygon.

That being said, the sum of interior angles of a polygon is-

[n – 2] × 180°

Where n refers to – number of sides of the polygon

As an example, for quadrilateral [4-2] × 180° = 360°

Note: The angle sum property of a polygon is applicable to both concave and convex polygon.

### Solved Examples

Let’s practice some quadrilateral problems and solution of understanding quadrilaterals class 8

Example1:

Find out the sum of the measures of the angles of a convex quadrilateral? Reasons why this property holds true if the quadrilateral is not convex? (Draw a non-convex quadrilateral and try!)

Solution1:

According to the Angle sum of a convex quadrilateral = (4 – 2) × 180° = 2 × 180° = 360°

Seeing that, a quadrilateral, which is concave, i.e. not convex has a similar number of sides i.e. 4 as a concave quadrilateral have, therefore, a quadrilateral which is not convex also holds this property. I.e. angle sum of a non-convex (concave) quadrilateral also equal to 360°

Above is a quadrilateral with sides ABCD, made of two triangles ▴ABC and ▴ADC. This means that the sum of all the interior angles of this quadrilateral will be equal to the sum of interior angles of two triangles i.e. 180° + 180° = 360°

Yes, the property holds true for a quadrilateral that is not convex since any quadrilateral can be split up into two triangles.

Example2:

Find out the angle sum of a polygon i.e. a heptagon with 7 numbers of sides?

Solution2:

Given number of sides = 7

Applying the rule to Angle sum of a polygon with 7 sides

= (7 – 2) × 180°

= 5 × 180°

= 900°

1. How Many Kinds of Quadrilaterals Are There?

There are a number of quadrilaterals that are named based on the characteristic of their sides and their angle. Check below the different types of quadrilateral;-

A. Trapezium

A trapezium is a type of a quadrilateral with one pair of parallel sides. Note that If the non-parallel sides of a trapezium measure the same then it is called an Isosceles Trapezium.

B. Kite

A kite is a type of a quadrilateral with two pairs of adjacent sides that measure the same.

C. Parallelogram

A parallelogram is a type of a quadrilateral with two pairs of opposite sides that are parallel to each other.

Remember that a rhombus, rectangle, and a square are also quadrilateral which also makes for a special type of parallelograms.

2. What Does a Measure of Sum of the Exterior Angles of a Polygon Dictate?

• The total of the exterior angles of any polygon equals 360°.

• It is applicable to regular and irregular, small and large polygons.