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TRIANGLE-SUM THEOREM During this lesson, you will: Find the sum of the angles of a triangle Use exterior angles of triangles Classify each triangle based upon its angle measures: ACUTE OBTUSE RIGHT EQUIANGULAR INVESTIGATION 3 INVESTIGATIVE RESULTS: THEOREM Triangle Sum Conjecture: The sum of the measures of the interior angles of any triangle is 180º ▲ Sum = 180. B A mA + m B + m C = 180 C Ex. 1 Z Find m Z X 48º mX + mY + mZ = 180 48 + 67 + mZ = 180 115 + mZ = 180 mZ = 65 67º Y Ex. 2 Find the values of a, b and c. C EX. 2 cº 70º Find c aº c + 70 = 90 A c = 20º D Find a. Use Triangle Sum a + mADC + c = 180 a + 90 + 20 = 180 a + 110 = 180 a = 70º bº B Find b. Use Triangle Sum b = 20º Use your triangle sum conjecture to calculate the measure of the third angle in each triangle below. Third Angle Conjecture: If two angles of one triangle are equal in measure to two angles of another triangle, then the remaining angles _____________________. 7 Exterior Angle Theorem Remote interior angles A B 2 Exterior angle 1 3 x C m x = m 1 + m 2 The measure of an exterior angle in any triangle equals the sum of the two remote interior angles. 1. Measure the angles of your triangle that you traced. 2. Extend one side of your triangle: 3. Measure that exterior angle Geometry Mrs. McConaughy 9 Examples:Justify your answer. x = ____ x x + y = _____ 30 x y 135 x = ____ x x x 90 45 144 x = ____