Angles and Triangles
Jan 20, 2016
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 - PowerPoint PPT Presentation
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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
Equilateral TriangleThe 3 corner angles are
60 degrees.
60
60
60
Isosceles TriangleTwo of the sides are of
equal length.
The third side is a differentlength
Isosceles Triangle
Two of the corner angles are equal.
The third angle is different.
Some more Isosceles Triangles...
These two sides are equal.
The angles where the equal sides meet the third side are equal.
The third angle is different in size.
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
In a right-angled triangle, one of The corner angles is a 90 degree angle.
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
180CBA
180
A
B C
Sample problem: work out the value of the angle x in the triangle shown.
90 45
x1804590 x
9045180 x
45x
What type of triangle is this?
Sample problem 2: work out the values of the angles x and y in the triangle shown.
12060 x
y
180120x
60x
18060 yx
6060180 y
60y
120180 x
1806060 y
What type of triangle is this?
Opposite AnglesWhen 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
60
x
y
Work out the value of the angles x and y in the diagram below.
Using the opposite angle rule, y and 60 are equal
60y
Using the alternate angle rule, y and x are equal
60x
125
y
Work out the value of the angles x and y in the diagram below.
x
Using the corresponding angle rule, y and 125 are equal
Using the straight angle rule, 180 yx
55125180 x
125y
180125x
55x
125
y
Work out the value of the angles x and y in the diagram below.
x
Using the interior angle rule, the angles shown add to 180⁰.So the angle in red is 55⁰.Using the opposite angle rule, 55x
55 55125180
Using the corresponding angle rule, 125y
105
105p
p105
Work out the value of the angle p in the diagram below.
The angles shown are corresponding angles.
Using the opposite angle rule,
Sample problem: the line L is parallel to side rs of the triangle, work out the angles x and y.
L
r sx
y52
42
Step1: As rs and L are parallel, we can use the alternate angle rule: 52x
Step2: Triangle rule: 18042yx
1804252 y
18094y 8694180y
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