TRIANGLE-SUM THEOREM

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 RIGHT EQUIANGULAR OBTUSE

INVESTIGATION

INVESTIGATIVE RESULTS: THEOREM Triangle Sum Conjecture: The sum of the measures of the interior angles of any triangle is 180º ▲ Sum = 180. B mA + m  B + m  C = 180 A C

Z Ex. 1 Find m Z 67º 48º Y X mX + mY + mZ = 180 48 + 67 + mZ = 180 115 + mZ = 180 mZ = 65

Ex. 2 C cº B bº aº A EX. 2 Find the values of a, b and c. 70º Find c c + 70 = 90 c = 20º D Find b. Use Triangle Sum Find a. Use Triangle Sum b = 20º a + mADC + c = 180 a + 90 + 20 = 180 a + 110 = 180 a = 70º

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 _____________________.

The measure of an exterior angle in any triangle equals the sum of the two remote interior angles. Exterior Angle Theorem Remote interior angles Exterior angle A BC 1 x 2 3 m x = m  1 + m  2

Measure the angles of your triangle that you traced. • Extend one side of your triangle: • Measure that exterior angle Mrs. McConaughy

Examples: Justify your answer. x = ____ 30 x x y 135 x + y = _____ x 144 x x = ____ x 90 45 x = ____

TRIANGLE-SUM THEOREM