Properties of Triangles

Properties of Triangles Types of Triangles Isosceles triangle 2 equal sides 2 equal angles (base) Equilateral Triangle 3 equal sides 3 equal angles. Scalene triangle 3 unequal sides 3 unequal angles

Any triangle containing a 90o angle is a right-angled triangle An isosceles or a scalene triangle may contain a right angle. Right-angled isosceles triangles. Right-angled scalene triangle.

Any triangle containing a 90o angle is a right-angled triangle Types of Triangles Equilateral Triangle 3 equal sides 3 equal angles. Isosceles triangle 2 equal sides 2 equal angles (base) Scalene triangle 3 unequal sides 3 unequal angles 1. 2. 3. 4. Any triangle containing a 90o angle is a right-angled triangle

The sum of the interior angles of a triangle is 180º. Angles in Triangles The sum of the interior angles of a triangle is 180º.

Calculate angles a, b and c Calculating unknown Angles Example 1 a 65o Calculate angle a. Angle a = 180 – (90 + 65) = 180 – 155 = 25o Example 2 Calculate angles a, b and c a b c Since the triangle is equilateral, angles a, b and c are all 60o (180/3)

Calculating unknown Angles Example 3 a 65o Calculate angle a. b Angle a = 65o (base angles of an isosceles triangle are equal). Angle b = 180 –(65 + 65) = 180 – 130 = 50o Example 4 Calculate angles x and y y 130o x

Calculate angles a and b. Calculating unknown Angles Example 5 Calculate angles a and b. b a Example 6 Calculate angle a 15o 27o a Angle a = 180 – (15 + 27) = 180 – 42 = 138o

Exterior Angles

What is the measure of x? 120°

What is the measure of D? 138°

Challenge: find x

Calculate all the angles in this star. Draw this diagram Calculate all the angles in this star. How many right-angled triangles angles? How many pairs of congruent triangles are there? *Not drawn accurately

D C 124° E x y A B Draw this diagram Identify 2 pairs of congruent isosceles triangles. Identify four pairs of congruent right-angled triangles. Calculate angles x and y. 124° D C A B E x y