1. Properties of Triangles

2. Properties of Triangles
Types of Triangles
Isosceles triangle
2 equal sides
2 equal angles (base)
Equilateral Triangle
3 equal sides
3 equal angles.
Scalene triangle
3 unequal sides
3 unequal angles

3. Any triangle containing a 90o angle is a right-angled triangle
An isosceles or a scalene triangle may contain a right angle.
Right-angled
isosceles triangles.
Right-angled
scalene triangle.

4. The angle sum of a triangle = 1800
To determine the angle sum of any Triangle
How can we use this to help us?
Take 3 identical copies of this triangle and put them together, so: 3 1 2
Angles on a straight line add to 180o
These are the same angles as in the triangle!
The angle sum of a triangle = 1800

5. 1. 2. 3. 4. 5. Types of Triangles Equilateral Triangle
3 equal sides
3 equal angles.
Isosceles triangle
2 equal sides
2 equal angles (base)
Scalene triangle
3 unequal sides
3 unequal angles 1. 2. 3. 4. 5.
Any triangle containing a 90o angle is a right-angled triangle
The angle sum of a triangle = 1800

6. Calculate angles a, b and c
Calculating unknown Angles
Example 1 a
65o
Calculate angle a.
Angle a = 180 – ( )
= 180 – 155 = 25o
Example 2
Calculate angles a, b and c a b c
Since the triangle is equilateral,
angles a, b and c are all 60o (180/3)

7. Calculating unknown Angles
Example 3 a
65o
Calculate angle a. b
Angle a = 65o (base angles of an isosceles triangle are equal).
Angle b = 180 –( )
= 180 – 130 = 50o
Example 4
Calculate angles x and y y
130o x

8. Calculate angles a and b.
Calculating unknown Angles
Example 5
Calculate angles a and b. b a
Example 6
Calculate angle a
15o
27o a
Angle a = 180 – ( )
= 180 – 42 = 138o

9. Properties of Triangles
Exterior Angles

10. Exterior Angle of a Triangle1.
Draw a triangle of any size
Extend one of the sides
Measure angle a and b
accurately using a protractor
Add angles a and b together
Measure angle c accurately
using a protractor
What do you notice? 2. b 3. c a 4. 5. 6.

11. Exterior Angles of a Triangle1.
Draw a second triangle of any size
Extend all of the sides
Measure angle a, b and c
accurately using a protractor
Add angles a, b and c together
What do you notice? a 2. 3. b 4. c 5.

12. Properties of Triangles

13. Copy and complete the following statements:
A triangle with all sides equal is called ...
A triangle with two sides equal is called ...
A triangle with no sides equal is called ...
A triangle with all angles equal is called ...
A triangle with two (base) angles equal is called ...
A triangle with one angle of 90° is called ...
An equilateral triangle has got all equal ... and ...
An isosceles triangle has got two equal ... and ...
Two triangles that are identical in shape and size are called ...

16. Calculate all the angles in this star.
Draw this diagram
Calculate all the angles in this star.
How many right-angled triangles angles?
How many pairs of congruent triangles are there?
*Not drawn accurately

18. D C
124° E x y A B

19. D C 124° E x y A B Draw this diagram
Identify 2 pairs of congruent isosceles triangles.
Identify four pairs of congruent right-angled triangles.
Calculate angles x and y.
124° D C A B E x y