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3.5: The Triangle Sum Theorem

3.5: The Triangle Sum Theorem. Expectations: G1.2.1: Prove that the angle sum of a triangle is 180 and that an exterior angle has measure equal to the sum of its remote interior angles. m. m is the only line through P parallel to l. The Parallel Postulate.

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3.5: The Triangle Sum Theorem

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  1. 3.5: The Triangle Sum Theorem Expectations: G1.2.1: Prove that the angle sum of a triangle is 180 and that an exterior angle has measure equal to the sum of its remote interior angles. 3.5: The Triangle Sum Theorem

  2. m m is the only line through P parallel to l. The Parallel Postulate • Given a line and a point not on the line, there is exactly one line through the point that is parallel to the given line. P l 3.5: The Triangle Sum Theorem

  3. Linear Triples • ∠ABC, ∠CBD and ∠DBE form a linear triple iff ∠ABC is adjacent to ∠CBD and ∠CBD is adjacent to ∠DBE such that BA and BE are opposite rays. 3.5: The Triangle Sum Theorem

  4. Linear Triples • ∠ABC, ∠CBD and ∠DBE form a linear triple C D A B E 3.5: The Triangle Sum Theorem

  5. Linear Triple Postulate • If three angles form a linear triple, then the sum of their measures is ______. 3.5: The Triangle Sum Theorem

  6. Triangle Sum Theorem • The sum of the measures of the angles of a triangle is _______. 3.5: The Triangle Sum Theorem

  7. Hint: Draw BD such that BD || AC. • Given: Triangle ABC with angles A, B and C. • Prove: m∠A + m∠B + m∠C = 180. 3.5: The Triangle Sum Theorem

  8. 3.5: The Triangle Sum Theorem

  9. 3.5: The Triangle Sum Theorem

  10. In triangle ABC, the measures of the angles satisfy the extended ratio 1:2:3. What are the measures of the angles? 3.5: The Triangle Sum Theorem

  11. Exterior and Remote Interior Angles of a Triangle The 3 angles of a triangle are also referred to as the interior angles of the triangle. Z X Y 3.5: The Triangle Sum Theorem

  12. Exterior and Remote Interior Angles of a Triangle If a side of the triangle is extended, an exterior angle is formed. Z ∠WYZ is an exterior angle for triangle XYZ X Y W 3.5: The Triangle Sum Theorem

  13. Exterior and Remote Interior Angles of a Triangle ∠X and ∠Z are remote interior angles with respect to ∠WYZ. Z X Y W 3.5: The Triangle Sum Theorem

  14. Exterior Angle Theorem • The measure of an exterior angle of a triangle is equal to the • Proof is a part of the assignment. 3.5: The Triangle Sum Theorem

  15. Assignment • pages 173-175, # 8 - 44 (all ≠ 40). 3.5: The Triangle Sum Theorem

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