Good Afternoon!
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Transcript of Good Afternoon!
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
CONFIDENTIAL 3
Review
Measuring angles in Degrees
We often measure degrees using a protractor.
The normal protractor measures 0° to 180°.
CONFIDENTIAL 4
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
CONFIDENTIAL 10
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
CONFIDENTIAL 12
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
CONFIDENTIAL 13
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°
CONFIDENTIAL 14
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
CONFIDENTIAL 15
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.
CONFIDENTIAL 17
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.
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
CONFIDENTIAL 20
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
CONFIDENTIAL 21
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