3. Triangles The sum of the measures of the angles of a triangle is 180 degrees. m A + m B + m C = 180 o A BC An angle formed by a side and an extension of a different side. Exterior Angle 1 Remote interior angles 23 For each exterior angle of a triangle, the two non adjacent interior angles are called its Remote Interior Angles. 58 o x o Find x o Ex. Exterior Angle: Triangle Sum Theorem: x = 32°

4. Classifying Triangles The measure of any exterior angle of a triangle equals the sum of its two remote interior angles 1 2 3 m 1 = m 2 + m 3 Equilateral: All sides congruent Isosceles: at least two sides congruent Scalene: no sides congruent By Sides Equiangular: all angles congruent Acute: all acute angles Right: one right angle Obtuse: one obtuse angle By Angles Exterior Angle Theorem: 2. Why can’t a triangle have two right or two obtuse angles? 1. Write an argument that proves the Exterior Angle Theorem 4

5. 1.Angle 1 and 4 form a Linear Pair (Given in the Picture) Angle 1 and 4 are Supplementary (Linear Pair Property) (Def. of Supplementary) (Triangle Sum Theorem) (Subtraction Property) (Substitution Property) 2. The Triangle Sum Theorem says that the sum of the angles of a triangle equals 180°. If a Triangle had two right or two obtuse angles then those two angles alone would be greater than or equal to 180°, leaving nothing left for the third angle.