 Properties of Triangles

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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.

Properties of Triangles
What do these symbols mean? right angle parallel to each other, but not parallel with the sides with only one arrow 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

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

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

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 Alternate angles are equal The internal angles are now on a straight line and therefore must add up to 180o a a b b Corresponding angles are equal

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

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