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DO NOW 1) 30 + 90 + X = 180 2) 55 + X + 105 = 180 3) X + 58 = 90 4) 31 + X = 90 Triangles, Triangles, and MORE Triangles Geometry Week 7 of 9 Unit 2: Angles and Angle Relationships 10/1 & 10/2 Standards & Objectives Standard 12.0 and 13.0 Objectives: To classify triangles and find the measures of their angles To use exterior angles of triangles ACTIVITY Draw and cut out a large triangle. Number the angles and tear them off. Place the three angles adjacent to each other to form one angle. 1) What kind of angle is formed by the three smaller angles? What is its measure? 2) Make a conjecture about the sum of the measures of the angles of a triangle. Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180. Different Types of Triangles There are several different types of triangles. You can classify a triangle by its sides and its angles. There are THREE different classifications for triangles based on their sides. There are FOUR different classifications for triangles based on their angles. Classifying Triangles by Their Sides EQUILATERAL – 3 congruent sides ISOSCELES – at least two sides congruent SCALENE – no sides congruent Classifying Triangles by Their Angles EQUIANGULAR – all angles are congruent ACUTE – all angles are acute EQUIANGULAR RIGHT – one right angle ACUTE RIGHT OBTUSE – one obtuse angle OBTUSE Can You Classify the Different Triangles in the Picture Below? Classify the following triangles: AED, ABC, ACD, ACE The Classifications… Triangle AED = Equilateral, Equiangular Triangle ABC = Equilateral, Equiangular Triangle ACD = Scalene, Obtuse Triangle ACE = Scalene, Right So how did you do? Triangle Exterior Angle Theorem The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. 2 1 3 EXAMPLE 40 30 X Measure of X = 40 + 30 Measure of X = 70 PRACTICE EXAMPLE X 113 113 = 70 + Measure of X 43 = Measure of X 70