Transcript Angles and Triangles - SMS Math Department

Angles and Triangles
Cian Taylor
Email: [email protected]
Web: http://eduspaces.net/ciantaylor
About me
• I am an Irish secondary school teacher of
Maths and Science.
• Check out my eduspace page at
http://eduspaces.net/ciantaylor
• Feel free to use this presentation for
educational purposes but please leave
the title slide with my contact details
intact.
Equilateral Triangle
Equilateral Triangle:
The 3 sides are of
equal length
Equilateral Triangle
60 
60 
Equilateral Triangle
The 3 corner angles are
60 degrees.
60 
Isosceles Triangle
Two of the sides are of
equal length.
The third side is a different
length
Isosceles Triangle
The third angle is different.
Two of the corner angles are
equal.
Some more Isosceles Triangles...
The third angle is different in size.
These two sides are equal.
The angles where the equal sides
meet the third side are equal.
Some more Isosceles Triangles...
Equal Sides
Equal Angles
Some more Isosceles Triangles...
Equal Sides
Which two angles are
equal?
Some more Isosceles Triangles...
Which two angles are
equal?
Scalene Triangle
All angles are different sizes.
All sides are different lengths.
Right-angled Triangle
In a right-angled triangle, one of
the corner angles is a 90 degree
angle.
90 degree angle.
More Right-angled Triangles
90 degree angle.
In a right-angled triangle, one of
The corner angles is a 90 degree
angle.
Angles in a Triangle
The angles of a triangle, added
together, form a straight angle, 180⁰.
This condition holds for any Triangle
(Right-angled).
180 
This condition holds for any Triangle
(Equilateral).
180 
Angles in a Triangle
(Isosceles)
180 
This condition holds for any Triangle
(Scalene).
180 
Using this rule
A
A  B  C  180 
B
C
180 
Sample problem: work out the value of
the angle x in the triangle shown.
x
90  45  x  180
x  180  45  90
x  45
90 
45 
What type of triangle is this?
Sample problem 2: work out the values of the angles x
and y in the triangle shown.
x  y  60  180
60  y  60  180
y
y  180 60  60
y  60
60 
x
What type of
triangle is this?
120 
x  120  180
x  180  120
x  60
Opposite Angles
When two lines intersect, 4 angles are formed.
Angles which are opposite each other, are equal.
The two angles in red are opposite angles, they are equal in size.
The two angles in yellow are opposite angles, they are equal in size.
Angles and parallel lines.
When a line crosses 2 parallel lines many
of the angles formed are equal.
The angles in red are all equal in size.
The angles in yellow are all equal in size.
Angles and parallel lines.
All the acute angles are equal and all the obtuse angles are equal.
Some of these angles have special names.
Corresponding Angles
Corresponding Angles are equal.
You can spot corresponding angles by
looking for the following shapes
You can spot corresponding angles by
looking for the following shapes
Corresponding Angles: ‘F’ shape
Alternate angles
Alternate angles are equal
You can spot alternate angles by
looking for the following shapes
Alternate Angles: ‘Z’ shape
Interior Angles
Interior Angles add to 180⁰
Angles and parallel lines.
Interior Angles
Interior Angles add to 180⁰
You can spot interior angles by
looking for the following shapes
Interior Angles: ‘C’ shape
Work out the value of the angles x and
y in the diagram below.
60 
y  60
y
x
x  60
Using the opposite angle rule, y and 60 are equal
Using the alternate angle rule, y and x are equal
Work out the value of the angles x and
y in the diagram below.
125 
x  55
x
y
y  125
Using the corresponding angle rule, y and 125 are equal
Using the straight angle rule, x  y  180
x  125  180
x  180  125  55
Work out the value of the angles x and
y in the diagram below.
125 
180   125   55
x
55 
y
Using the interior angle rule, the angles shown add to 180⁰.
So the angle in red is 55⁰.
x  55
Using the opposite angle rule,
Using the corresponding angle rule,
y  125
Work out the value of the angle p in
the diagram below.
105 
105 
p
The angles shown are corresponding angles.
Using the opposite angle rule, p  105
Sample problem: the line L is parallel to side rs
of the triangle, work out the angles x and y.
52 
x
r
L
y
42 
s
Step1: As rs and L are parallel, we can use the
alternate angle rule: x  52
Step2: Triangle rule: x  y  42  180
52  y  42  180
y  94  180 y  180  94  86