CONFIDENTIAL 1

Good Afternoon!

Today we will be learning about Quadrilaterals and other polygons

(rectangle,square, rhombus, parallelogram,

trapezoid)Let’s warm up :

Angles of the triangle is given.What type of triangles are the following?

1) 53º, 55º and 72º.

2) 110º, 65º and 5º.

3) 26º, 90º and 64º.

4) 45º, 90º and 45º.

1) Acute triangle

2) Obtuse triangle

3) Right triangle

4) Right Isosceles triangle

CONFIDENTIAL 2

A triangle is one of the basic shapes of geometry: A polygon with three corners or vertices

and three sides or edges which are line segments.

We learnt about triangles.

The three angles always add to 180°.

vertex

arm

B

A

Ccb

a

angle ACBOr

angle c

Let’s review what we did in the last session

CONFIDENTIAL 3

Interior Angle: An Interior Angle is an angle inside a shape.

Interior Angle

Exterior Angle

45°135°

Exterior Angle: The Exterior Angle is the angle between any side of a shape, and a line extended from

the next side.

If you add up the Interior Angle and Exterior Angle you get a straight line, 180°.

Review

CONFIDENTIAL 4

The basic elements of any triangle are its sides and vertices. Triangles are classified depending on relative sizes of their

elements.

Triangles can be classified according to their internal angles.

Acute Triangle: An acute triangle is a triangle whose angles are all acute (i.e. less

than 90°).

B

A

Cc

ba

In the acute triangle shown above, a, b and c are all acute angles.

Triangle Classification

Review

CONFIDENTIAL 5

Right Triangle: A right triangle is a triangle with a right angle (i.e. 90°).

hypotenuse

The side opposite the right angle is always the triangle's longest side.It is called the hypotenuse of the triangle.

The other two sides are called the legs.

leg

leg

b°90°

a°

right angle

Review

CONFIDENTIAL 6

Obtuse Triangle: An obtuse triangle has one obtuse angle (i.e. greater than 90º).

The longest side is always opposite the obtuse angle.

In the obtuse triangle shown above, a is the obtuse angle.

>90°

a°

b°

Review

CONFIDENTIAL 7

The triangle classification is summarized as follows:

There are three special names given to triangles that tell how many sides (or angles)

are equal.

Equilateral Triangle: An equilateral triangle has all three sides equal in length. Its three

angles are also equal and they are each 60º.

a

aa

60º 60º

60º

Types of Triangles

Review

CONFIDENTIAL 8

Isosceles Triangle: An isosceles triangle has two sides of equal length. The angles opposite the equal sides are also equal.

a a

xº xº

Scalene Triangle: A scalene triangle has no sides of equal length. Its angles are also all

different in size.

a

b

c

xº

yº

zº

Review

CONFIDENTIAL 9

Combining the Names

Right Isosceles Triangle:One right angle.Two equal sides.Two other equal angles always of 45°.

Right Scalene Triangle:One right angle.No equal sides.Two other unequal angles.

There are two types of right angled triangle:

Remember the little square in the triangle tells us that it is a right angled triangle.

Review

CONFIDENTIAL 10

Let’s start withQuadrilaterals and other polygons (rectangle,square, rhombus, parallelogram, trapezoid)

A polygon is a plane shape with straight sides.

Types of Polygons

Simple or Complex: A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself.

Simple Polygon

Complex

Polygon

CONFIDENTIAL 11

Concave or Convex: A convex polygon has no angles pointing inwards. More

precisely, no internal angles can be more than 180°.

If there are any internal angles greater than 180° then it is concave.

Regular or Irregular: If all angles are equal and all sides are equal, then it is regular, otherwise it is

irregular .

convex Polygon

concave Polygon

regular Polygon

irregular Polygon

CONFIDENTIAL 12

Names of Polygons

Name Sides Shape

Triangle 3

Quadrilateral 4

Pentagon 5

Hexagon 6

Heptagon 7

Octagon 8

Nonagon 9

Decagon 10

CONFIDENTIAL 13

There are many different kinds of quadrilaterals, but all have several things in common: all of them have

four sides, are coplanar, have two diagonals, and the sum of their four interior angles equals 360

degrees.

But the sides have to be straight, and it has to be 2-dimensional.

We will learn about quadrilateral today.

A quadrilateral is a 4-sided polygon, just like a triangle is a 3-sided polygon, a

pentagon is a 5-sided polygon, and so on.

CONFIDENTIAL 14

Types of Quadrilaterals

There are special types of quadrilateral :

the rectangle

the rhombus

the square

the kite

those are all parallelograms

CONFIDENTIAL 15

Also opposite sides are parallel and of equal length.

The Rhombus: A rhombus is a four-sided shape where all sides have equal length.

a

cbd

The Rectangle: A rectangle is a four-sided shape where every angle is a right angle (i.e.

90°).

CONFIDENTIAL 16

The Square: A Square is a four-sided shape which has all the sides equal and where every

angle is a right angle (i.e. 90°).

Also opposite sides of a square are parallel.

A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal

length).

CONFIDENTIAL 17

The Parallelogram: Opposite sides are parallel and equal in length, and opposite angles are

equal (angles "a" are the same, and angles "b" are the same).

a

b a

b

The Trapezoid (or Trapezium): A trapezoid has one pair of opposite sides parallel.

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

A trapezoid is not a parallelogram because only one pair of sides is parallel.

CONFIDENTIAL 18

BREAK

CONFIDENTIAL 19

GAME

Click on the link below for some exciting puzzle

http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw-puzzles/12-piece-jigsaw/010306snowman.html

CONFIDENTIAL 20

Assignments

Classify each quadrilaterals as rectangle,square, rhombus, parallelogram, trapezoid:

a

c b

d

ab

ab

1) 2)

3)

1) rhombus2) parallelogram

3) trapezoid

CONFIDENTIAL 21

Classify each quadrilaterals as rectangle,square, rhombus, parallelogram, trapezoid:

a

b

a

b

4) 5)

6) 7)

4) rectangle5) trapezoid

6) square7) parallelogram

CONFIDENTIAL 22

Write the given figure is a polygon or not a polygon.

8) 9)

10)

8) Polygon 9) Not a Polygon (has a curve)

10) Not a Polygon (open, not closed)

CONFIDENTIAL 23

A polygon is a plane shape with straight sides.

Types of Polygons

Simple or Complex: A simple polygon has only one boundary, and it doesn't cross over itself. A complex polygon intersects itself!

Simple Polygon

Complex

Polygon

Very Good!Let's Review

CONFIDENTIAL 24

Concave or Convex: A convex polygon has no angles pointing inwards. More

precisely, no internal angles can be more than 180°.

If there are any internal angles greater than 180° then it is concave.

Regular or Irregular: If all angles are equal and all sides are equal, then it is regular, otherwise it is

irregular .

convex Polygon

concave Polygon

Regular Polygon

Irregular Polygon

CONFIDENTIAL 25

Names of Polygons

Name Sides Shape

Triangle 3

Quadrilateral 4

Pentagon 5

Hexagon 6

Heptagon 7

Octagon 8

Nonagon 9

Decagon 10

CONFIDENTIAL 26

There are many different kinds of quadrilaterals, but all have several things in common: all of them have

four sides, are coplanar, have two diagonals, and the sum of their four interior angles equals 360

degrees.

But the sides have to be straight, and it has to be 2-dimensional.

A quadrilateral is a 4-sided polygon, just like a triangle is a 3-sided polygon, a

pentagon is a 5-sided polygon, and so on.

Review

CONFIDENTIAL 27

Also opposite sides are parallel and of equal length.

The Rhombus: A rhombus is a four-sided shape where all sides have equal length.

a

cbd

The Rectangle: A rectangle is a four-sided shape where every angle is a right angle (i.e.

90°).

Review

Types of Quadrilaterals

CONFIDENTIAL 28

The Square: A Square is a four-sided shape which has all the sides equal and where every

angle is a right angle (i.e. 90°).

Also opposite sides of a square are parallel.

A square also fits the definition of a rectangle (all angles are 90°), and a rhombus (all sides are equal

length).

Review

CONFIDENTIAL 29

The Parallelogram: Opposite sides are parallel and equal in length, and opposite angles are

equal (angles "a" are the same, and angles "b" are the same).

a

b a

b

The Trapezoid (or Trapezium): A trapezoid has one pair of opposite sides parallel.

NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!

A trapezoid is not a parallelogram because only one pair of sides is parallel.

Review

CONFIDENTIAL 30

You have done a nice job.See you in the next session.