1. Properties of Triangles
Objectives:
E Grade Show that the angles of a triangle add up to 180o
and use this to find angles.
Show that the exterior angle of a triangle is equal
to the sum of the interior opposite angles.
Use angle properties of isosceles, equilateral
and right-angled triangles.

2. Properties of Triangles
Using the symbols describing shapes answer the following questions:
36o a b c
45o d
Isosceles triangle
Two angles are equal
Equilateral triangle
all angles are equal
Right-angled triangle
a = 36o
c = 180 ÷ 3 = 60o
d = 180 – ( )
= 45o
b = 180 – (2 × 36)
= 108o

3. Properties of Trianglesq
36o p s r
56o
Example
Made up of 2 isosceles triangles
p = 38o
q = 180 – (2 × 38) = 104o
56 + (r + s) = 180o
(r + s) = 180 – 56 = 124
Because r = s
r = s = 124 ÷ 2 = 62o

4. Properties of Triangles
Now do these:
h = i
Equilateral triangle
h + i =
a = 64o
c = d
e = f = g = 60o
h + i = 90
b = 180 – (2 ×64o ) = 52o
c + d =
c = d = 45o
c + d = 108
c = d = 54o
p = 50o
q = 180 – (2 ×50o ) = 80o
r = q = 80o
vertically opposite angles are equal
Therefore : s = t = p = 50o

5. Properties of Triangles
p = q = r = 60o
e = f = g = 60o
d = 180 – 60 = 120o
s = t = = 68.5o 2
e + 18 = a = 60
external angle = sum of opposite internal angles
e = 60 – 18 = 42o

6. Properties of Triangles
Worksheet