Properties of Triangles

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: b 45o d a c 36o Equilateral triangle all angles are equal Isosceles triangle Two angles are equal Right-angled triangle c = 180 ÷ 3 = 60o a = 36o d = 180 – (45 + 90) = 45o b = 180 – (2 × 36) = 108o

3. Properties of Triangles Example Made up of 2 isosceles triangles p = 38o q 36o s q = 180 – (2 × 38) = 104o p r 56 + (r + s) = 180o 56o (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 = 180 - 90 a = 64o c = d e = f = g = 60o h + i = 90 b = 180 – (2 ×64o ) = 52o c + d = 180 - 72 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 = 180 - 43= 68.5o 2 e + 18 = a = 60 external angle = sum of opposite internal angles e = 60 – 18 = 42o

6. Worksheet Properties of Triangles