Properties of Triangles Objectives G Grade Identify isosceles

Properties of Triangles Objectives: G Grade Identify isosceles, equilateral and right-angled triangles. Use the word ‘congruent’ when triangles are identical. E Grade Show that the angles of a triangle add up to 180 o 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 C c A a b B When a side of a polygon is extended an exterior angle is created We know that the sum of internal angles (a + b + c) = 180 o We also know that angles on a line add up to 180 o Therefore if: a + c + b = 180 o and b + external angle = 180 o The external angle = a + c

Properties of Triangles Example y x is an exterior angle so x = 39 + 81 = 120 o x 81 o 39 o x is again an exterior angle so 120 = y + 90 so y = 30 o

Now do these: Properties of Triangles c = 63 + 74 = 137 o d = 180 - 63 = 113 o e = 180 - 74 = 106 o a = 42 + 40 = 82 o b = 138 - 48 = 90 o 132 = x + 90 x = 42 o

Properties of Triangles Now do these: p = 49 + 63 = 112 o q = 49 + 76 = 125 o r = 140 - 32 = 108 o 180 - 140 = 40 o 180 - 118 = 62 o s = 180 – (40 + 62) = 78 o Bearing 131 + 180 =311 o x = 131 - 90 = 41 o or 270 + 41 =311 o

Worksheet Properties of Triangles