Properties of Triangles 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 equalto the sum of the interior opposite angles.

Use angle properties of isosceles, equilateral and right-angled triangles.

Properties of Triangles Properties of Triangles

Using the symbols describing shapes answer the following questions:

36o a

b

c

45o

d

Isosceles triangleTwo angles are equal

a = 36o

b = 180 – (2 × 36) = 108o

Equilateral triangleall angles are equal

c = 180 ÷ 3 = 60o

Right-angled triangle

d = 180 – (45 + 90) = 45o

Properties of Triangles Properties of Triangles

Example

q 36o

p

s

r

56o

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

Properties of Triangles Properties of Triangles Now do these:

a = 64o

b = 180 – (2 ×64o ) = 52oc = dc + d = 180 - 72c + d = 108c = d = 54o

Equilateral trianglee = f = g = 60o

h = ih + i = 180 - 90h + i = 90c = d = 45o

p = 50o

q = 180 – (2 ×50o ) = 80o

r = q = 80o vertically opposite angles are equalTherefore : s = t = p = 50o

Properties of Triangles Properties of Triangles

e = f = g = 60o

d = 180 – 60 = 120o

e + 18 = a = 60

external angle = sum of opposite internal angles

e = 60 – 18 = 42o

p = q = r = 60o

s = t = 180 - 43 = 68.5o

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