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November 22, 2011 4.2 Angle Relationships in Triangles Sum Theorem: The sum of the interior angles of a triangle is 180 A m A + m B + m C = 180 C B November 22, 2011 Proof of Triangle Sum Theorem Given: AD II BC Prove: m 1 + m 2 + m 3 = 180 Statement Reason November 22, 2011 1. 60 70 55 November 22, 2011 2. corollary: The measure of each angle of an equiangular triangle is 60o. Corollary: a theorem in which the proof follows directly from another theorem. November 22, 2011 Find x. 3. Corollary: The acute angles of a right triangle are complementary. November 22, 2011 Corollary: The acute angles of a right triangle are complementary. Proof: Given: Prove: ABC is right with rt A comp. C Statements B Reasons November 22, 2011 4 5 6 interior angles: 1, 2, 3 exterior angles: 4, 5, 6 remote interior: interior angle that is not adjacent to the exterior angle. November 22, 2011 80 60 x November 22, 2011 Examples. Find x. 1. 2. 80 x 3. 3x-22 November 22, 2011 E C D A F B November 22, 2011 Third Angles Theorem: If 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent. ex. 4y2 6y2-40 November 22, 2011 Examples. 1. The measure of one acute angle of a right triangle is one-fourth the measure of the other acute angle. Find the angles. 2. The ratio of the measures of a triangle are 3:2:1. Find the measure of each angle.