TRIANGLE-SUM THEOREM During this lesson, you will:  Find the sum of the angles of a triangle  Use exterior angles of triangles.

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Presentation transcript:

TRIANGLE-SUM THEOREM During this lesson, you will:  Find the sum of the angles of a triangle  Use exterior angles of triangles

EQUIANGULAR OBTUSE RIGHTACUTE Classify each triangle based upon its angle measures:

INVESTIGATION 3

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

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

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

7 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 _____________________.

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

GeometryMrs. McConaughy 9 1.Measure the angles of your triangle that you traced. 2.Extend one side of your triangle: 3.Measure that exterior angle

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