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3-4 Angles of a Triangle • A Triangle is a figure formed by three segments joining three noncollinear points. • 1) Classifying triangles by their sides. • a) Equilateral triangle • – 3 congruent sides • b) Isosceles triangle • - 2 congruent sides • c) Scalene triangle • - No congruent sides • 2) Classifying triangles by their angles. • a) Acute triangle • - has 3 Acute angles • b) Equiangular triangle • - has 3 congruent angles • - an Equiangular triangle is also Acute. • c) Right triangle • - has one right angle • d) Obtuse triangle • - has one obtuse angle Theorems: • 1) Theorem 3 - 11 Triangles Sum Theorem • The sum of the measures of the interior angles of a triangle is 180° • 2) Theorem 3 - 12 Exterior Angle Theorem • The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. B Ex. 1 C m<1 = m<B + m<C Problems: • 1) Classify the triangle • a) b) 60 60 60 46 88 46 • 2) Find the value of x. Then find the measure of the exterior angle. x0 72 0 (2 x 11) 0 • C) Corollary – to a theorem is a statement that can be proved easily using the theorem. • Corollary 4 to the triangle sum theorem. • The acute angles of a right triangle are complementary. C m<A + m<C = 90° B A • 3) The measure of one acute angle of a right triangle is one-fourth the measure of the other acute angle. Find the measure of each acute angle. x0 1 0 x 4 • Corollary 1 • If two angles of one triangle are to two angles of another triangle, then the third angles are . Corollary 2 • Each angle of an equiangular triangle has a measure of 60° • Corollary 3 • In a triangle, there can be at most one right angle or one obtuse angle. • Find the values of x and y. • 1) 2)