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Transcript

Today you will Apply the triangle angle-sum theorem and the exterior angle theorem 4.2 Angles of Triangles Triangle Angle-Sum Theorem: The sum of the interior angles of a triangle is 180 o A o m A + m B + m C = 180 C B Proof of the Triangle Angle-Sum Theorem: This proof uses an Auxiliary Line (an extra line drawn to help analyze geometric relationships). Given: ABC Prove: m 1 + m 2+m 3 = 180 5. Def. of Supplementary s 1. 2. Draw AD through A parallel to BC 2. 3. 4 and BAD are a linear pair 3. 4. 4 and BAD are suppl. BAD = m 2 + m 5 6. 7. m 4 + m 2 + m 5 = 180 7. 1 and 5 9. m 4 = m 1, m 5 = m 10. > 4. 5. 4 1 Reasons ABC 8. 2 5 C Statements 6. m 4 D 3 B 1. A > 3 8. 3 9. 10. Find each missing angle measure. 60 70 55 4 interior angles: 1, 2, 3 exterior angles: 4, 5, 6 5 6 remote interior: interior angle that is not adjacent to the exterior angle. So angle five's remote interior angles are A 1 C B If m 1 = 140, find m ACB Now find m A + m B Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Corollary: a theorem in which the proof follows directly from another theorem. Triangle Angle-Sum Corollaries: The acute angles of a right triangle are complementary. There can be at most one right or one obtuse angle in a triangle. Proof of Triangle Angle Sum Corollary: Proof: Given: Prove: ABC is right with rt A comp. C Statements B Reasons