Properties of Triangles

1. Properties of Triangles Objectives: Identify isosceles, equilateral and right-angled triangles. Use the word ‘congruent’ when triangles are identical. 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 What do these symbols mean? parallel to each other, but not parallel with the sides with only one arrow right angle parallel to each other same length as each other same length as each other, but not the same length as the sides with only one dash

3. Properties of Triangles What are the names and properties of these triangles ? Isosceles: 2 sides the same length 2 angles the same Equilateral: All sides the same length All angles the same (60o) Right-angled: Sides can be any length One angle 90o Scalene: All the sides are different lengths All the angles are different

4. Properties of Triangles Congruent: means all angles and lengths are the same. It can be a rotation e j a g f d i b h c Which shapes are congruent?

5. Properties of Triangles Proof that the internal angles in a triangle add up to 180o a b Add a line parallel to one of the sides The internal angles are now on a straight line and therefore must add up to 180o Alternate angles are equal a a b b Corresponding angles are equal

6. Properties of Triangles Now do these: 41o b 34o 62o 80o 54o a c 30o b = 180 – (54+41) = 85 c = 180 – (62+34) = 84 a = 180 – (80+30) = 70 79o y x z 141o 57o q p 58o p = 180 – (90+57) = 33 x = 180 – 141 = 39 r (vertically opposite angles are equal) q = 57 y = 180 – (58+39) = 83 r = 180 – (79+57) = 44 z = 180 – 83 = 97

7. Properties of Triangles 68o e a 17o 46o c b 39o d a = 180 – 90 = 90 d = 180 – (90+46) = 44 b = 180 – (90+39) = 51 c = 180 – (90+68) = 22 Think big triangle e = 180 – (90+44+17) = 29