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Understanding Triangle Properties: Isosceles, Equilateral, and Right-Angled Triangles

This resource introduces students to triangle properties, including identification of isosceles, equilateral, and right-angled triangles. Learn to apply the concept of congruence for identical triangles. Discover how the sum of interior angles equals 180° and how the exterior angle relates to opposite angles. Engage with practical examples and exercises that reinforce understanding of angle properties. Perfect for enhancing geometry skills in the classroom or at home.

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Understanding Triangle Properties: Isosceles, Equilateral, and Right-Angled Triangles

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  1. 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 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 C c b a A 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) = 180o We also know that angles on a line add up to 180o Therefore if: a + c + b = 180o and b + external angle = 180o The external angle = a + c

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

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

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

  6. Properties of Triangles Worksheet

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