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The Triangle Sum Theorem

The Triangle Sum Theorem. The Triangle Sum Theorem. The sum of the measures of the angles of a triangle are equal to 180 degrees. < 5 = < 3 and < 4= < 1 because alternate interior angles are congruent. Since <1+ < 2+ < 3=180 degrees then the sum of the interior angles is 180. 1. 3. 2. 4. 5.

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The Triangle Sum Theorem

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  1. The Triangle Sum Theorem

  2. The Triangle Sum Theorem • The sum of the measures of the angles of a triangle are equal to 180 degrees. < 5 = < 3 and < 4= < 1 because alternate interior angles are congruent. Since <1+ < 2+ < 3=180 degrees then the sum of the interior angles is 180. 1 3 2 4 5

  3. Definition of Remote Interior Angles • An Interior angle of a triangle that is not adjacent to a given exterior angle. • Ex. Angles 1 and 2 are remote Interior angles of angle 4. 2 3 4 1

  4. Exterior Angle Theorem • The Exterior Angle equals the sum of the two remote interior angles. (remote interior angles don’t touch the exterior angle). < 4 equals the sum of <1 +<2 . 50+70= 120 so <4= 120° 50° 1 70° 2 4 3

  5. Homework • p.189(15-27) all • you MUST copy the pictures!!!!!!

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