59: Proof of the Angle Sum Theorem

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5-9 Proof of the Angle Sum Theorem

• Objectives
• Prove that the sum of the angles in a triangle
  equals 180
• To prove the corollary to the angle sum theory
• To use the angle sum theorem and its corollary to
  determine the measures of unknown angles of a
  triangle.

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Angle Sum Vocabulary

• Corollary A conclusion that follows easily from
  a given theorem.
• Exterior Angle Angle formed by extending one
  side of a triangle through any vertex.

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Theorems

• Angle Sum Theorem The sum of the angle measures
  in any triangle is 180
• PROVE IT!
• x x y 180 (Triangle)
• y y y 180 (Line)
• y x (Alternate Interior Angles)

Transversal
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Theorems

• Corollary to the Angle Sum Theorem If ?ABC is
  any triangle, then an exterior angle of ABC has
  the same measure as the sum of the measures of
  the two nonadjacent interior angles.
• PROVE IT!
• m 1 m 2 m 3

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