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. Any triangle containing a 90o angle is a right-angled triangle
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.
Any triangle containing a 90o angle is a right-angled triangle

5. The sum of the interior angles of a triangle is 180º.
Angles in Triangles
The sum of the interior angles of a triangle is 180º.

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. Exterior Angles

10. What is the measure of x?
120°

11. What is the measure of D?
138°

12. Challenge: find x

14. 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

16. 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