CH. 4.1 APPLY TRIANGLE SUM PROPERTIES. VOCAB Interior Angles : angles inside the triangle (sum = 180) Exterior Angles: angles outside the triangle Interior.

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Presentation transcript:

CH. 4.1 APPLY TRIANGLE SUM PROPERTIES

VOCAB Interior Angles : angles inside the triangle (sum = 180) Exterior Angles: angles outside the triangle Interior angles exterior angle exterior angle exterior angle

CLASSIFYING BY SIDES SCALENEISOSCELES EQUILATERAL _____ CONGRUENT SIDES _____ CONGRUENT SIDES _____ CONGRUENT SIDES

CLASSIFYING BY SIDES SCALENEISOSCELES EQUILATERAL ____ CONGRUENT SIDES _____ CONGRUENT SIDES _____ CONGRUENT SIDES 0 2 3

CLASSIFYING BY ANGLES OBTUSE EQUIANGULAR _____ ACUTE ANGLES ACUTE _____ ACUTE ANGLES _____ ACUTE ANGLES RIGHT _____ ACUTE ANGLES

CLASSIFYING BY ANGLES OBTUSE EQUIANGULAR _____ ACUTE ANGLES ACUTE _____ ACUTE ANGLES _____ ACUTE ANGLES RIGHT _____ ACUTE ANGLES

THEOREM 4.1: TRIANGLE SUM THEOREM The sum of the measures of the interior angles of a triangle is ________. CA B m<A + m<B + m<C = ______

THEOREM 4.1: TRIANGLE SUM THEOREM The sum of the measures of the interior angles of a triangle is ________. CA B m<A + m<B + m<C = ______ 180

THEOREM 4.1: TRIANGLE SUM THEOREM EX. C A B m<A + m<B + m<C = x

THEOREM 4.1: TRIANGLE SUM THEOREM EX. C A B m<A + m<B + m<C = x = x = x = x

THEOREM 4.2: EXTERIOR ANGLE THEOREM The MEASURE OF AN EXTERIOR ANGLE OF A TRIANGLE IS EQUAL TO THE SUM OF THE MEASURES OF THE TWO ________ ANGLES. C A B m<1 = m<__ + m<__ 1

THEOREM 4.2: EXTERIOR ANGLE THEOREM The MEASURE OF AN EXTERIOR ANGLE OF A TRIANGLE IS EQUAL TO THE SUM OF THE MEASURES OF THE TWO __________________ ANGLES. C A B m<1 = m<__ + m<__ nonadjacent A B 1

THEOREM 4.2: EXTERIOR ANGLE THEOREM EX. C A B m<1 = m<A + m<B

THEOREM 4.2: EXTERIOR ANGLE THEOREM EX. C A B m<1 = m<A + m<B m<1 = m<1 =

EXAMPLE 3 C A B m<1 = m<A + m<B 3x - 9 x 73 D

EXAMPLE 3 C A B m<1 = m<A + m<B 3x – 9 = x + 73  move small x to big x - x -x 2x – 9 = 73  solve for x x – 9 = 2x = 82x = 41 so, 3(41) – 9 = x - 9 x 73 D

COROLLARY TO THE TRIANGLE SUM THEOREM THE ACUTE ANGLES OF A RIGHT TRIANGLE ARE ____________________. C A B m<A + m<B = ______

COROLLARY TO THE TRIANGLE SUM THEOREM THE ACUTE ANGLES OF A RIGHT TRIANGLE ARE ____________________. C A B m<A + m<B = ______ COMPLEMENTARY 90 = 90

COROLLARY TO THE TRIANGLE SUM THEOREM EX. C A B m<A + m<B = 90 x 27

COROLLARY TO THE TRIANGLE SUM THEOREM EX. C A B m<A + m<B = x = x = 63 x 27