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Transcript
Triangle Sum Theorem Geometry Angles of a Triangle Angles – when the sides of a triangle are extended Interior Angles • The three original angles • Interior - Inside Exterior Angles • The angles that are adjacent to the interior angles • Exterior - Outside TRIANGLE SUM THEOREM The sum of the measures of the interior angles of a triangle is 180 degrees. Proving the Triangle-Sum Theorem The proof of the Triangle-Sum Theorem requires the use of an auxiliary line. • An auxiliary line is an extra line or segment drawn in a figure to help analyze geometric relationships. • Any properties of an auxiliary line that you draw must be justified Proving the Triangle-Sum Theorem Given: ∆ABC Prove: m∠1 + ∠2 + m∠3 = 180 COROLLARY TO A THEOREM A corollary to a theorem is a statement that can be proved easily using the theorem. Corollaries can be used as a reason in a proof. COROLLARY TO THE TRIANGLE SUM THEOREM The acute angles of a right triangle are complementary.
