Angles and Triangles

Angles and Triangles

Cian TaylorEmail: cian.taylor@ireland.com

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

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