CONFIDENTIAL 1

Good Afternoon!

Today we will be learning about Triangles (isosceles, equilateral, right)

Let’s warm up :

3) What is the Complement of 35° ?

4) What is the Supplement of 66° ?

Find the missing angle around a point:

1) 40° + 110° + a° + 40° = 360°

2) 35° + 95° + b° + 70° = 360°

1) 170 °

2) 160 °

3) 55 °

4) 114 °

CONFIDENTIAL 2

Let’s review what we did in the last session

What Is an Angle?

An angle is a combination of two rays with a common endpoint.

The endpoint (O) is known as the vertex of the angle And

the rays (OA and OB) are called the sides or arms of the angle .

OA

B

angle AOB

vertex

arm

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Review

Measuring angles in Degrees

We often measure degrees using a protractor.

The normal protractor measures 0° to 180°.

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Review

Angles On a Straight Line

If we know one angle is 45°, what is angle “x" ?

45°x

Angle x will be 180° − 45° = 135°

This method can be used to find angles on one side of a straight line.

CONFIDENTIAL 5

Review

Angles Around a Point

40°

110°

60°150°

Angles around a point will always add up to 360 degrees.

The angles here all add to 360°.

40° + 110° + 150° + 60° = 360°

Because of this, if there is an unknown angle we can always find it.

CONFIDENTIAL 6

Review

Complementary Angles

Two Angles are Complementary if they add up to 90 degrees (a Right Angle).

60°

30°

These two angles (40° and 50°) are Complementary Angles, because they add up to 90°.

But the angles don't have to be together to Complement each other.

CONFIDENTIAL 7

Review

Supplementary Angles

Two Angles are Supplementary if they add up to 180 degrees (a Straight Angle).

120°60°

These two angles (120° and 60°) are Supplementary Angles, because they add up

to 180°.

But the angles don't have to be together to Supplement each other.

CONFIDENTIAL 8

Let’s start withTriangles (isosceles, equilateral, right)

A polygon is a plane (2-dimensional ) shape.Polygon is made of straight lines, and the shape is "closed" .

Example: Triangle, Quadrilateral, Pentagon.

Triangle Quadrilateral Pentagon

CONFIDENTIAL 9

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.

Today we will learn about triangles.

The three angles always add to 180°.

vertex

arm

B

A

Ccb

a

angle ACBOr

angle c

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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°.

CONFIDENTIAL 11

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

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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

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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°

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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

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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

CONFIDENTIAL 16

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.

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A triangle has angles 46º, 63º and 71º.What type of triangle is this?

Since all its angles are less than 90°, it is an acute triangle.

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BREAK

CONFIDENTIAL 19

GAME

Click on the link below for some exciting puzzle

http://www.thekidzpage.com/onlinejigsawpuzzles/jigsaw-puzzles/12-piece-jigsaw/03-04-06-jewels.html

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Assignments

Classify each triangle as Equilateral, Isosceles or Scalene :

2cm

2cm2cm 4 cm 4 cm

5cm

7 cm

3 cm

1) 2)

3)

1) Equilateral triangle 2) Isosceles triangle

3) Scalene triangle

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Classify each triangle as Acute, Right or Obtuse :

95 º 30º

90º

60º

60º 60º

60º

4) 5)

6)

4) Obtuse triangle

5) Right triangle

6) Acute triangle

CONFIDENTIAL 22

Angles of the triangle are given.What type of triangles are the

following?

7) 56º, 50º and 74º.

8) 105º, 48º and 27º.

9) 35º, 90º and 55º.

10) 60º, 60º and 60º.

11) 45º, 90º and 45º.

12) 36º, 64º and 90º.

7) Acute triangle

9) Right triangle

8) Obtuse triangle

10) Equilateral triangle

11) Right Isosceles triangle

12) Right Scalene triangle

CONFIDENTIAL 23

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.

Today we learnt about triangles.

The three angles always add to 180°.

vertex

arm

B

A

Ccb

a

angle ACBOr

angle c

Very Good!Let's Review

CONFIDENTIAL 24

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 25

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 26

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 27

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 28

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 29

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 30

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 31

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