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Proving the Interior Angle Sum Theorem

Proving the Interior Angle Sum Theorem. Adapted from Walch Education. Triangles Classified by Angle Measure. Triangles Classified by Side Lengths. Triangle Sum Theorem. Triangle Sum Theorem. The Triangle Sum Theorem can be proven using the Parallel Postulate .

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Proving the Interior Angle Sum Theorem

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  1. Proving the Interior Angle Sum Theorem Adapted from Walch Education

  2. Triangles Classified by Angle Measure 1.9.1: Proving the Interior Angle Sum Theorem

  3. Triangles Classified by Side Lengths 1.9.1: Proving the Interior Angle Sum Theorem

  4. Triangle Sum Theorem 1.9.1: Proving the Interior Angle Sum Theorem

  5. Triangle Sum Theorem • The Triangle Sum Theorem can be proven using the Parallel Postulate. • The Parallel Postulate states that if a line can be created through a point not on a given line, then that line will be parallel to the given line. • This postulate allows us to create a line parallel to one side of a triangle to prove angle relationships. 1.9.1: Proving the Interior Angle Sum Theorem

  6. Parallel Postulate 1.9.1: Proving the Interior Angle Sum Theorem

  7. Interior Angles, Exterior Angles, and Remote Interior Angles • Interior angles: ∠A, ∠B, and ∠C • Exterior angle: ∠D • Remote interior angles of ∠D: ∠A and ∠B • Notice that ∠C and ∠D are supplementary; that is, together they create a line and sum to 180˚. 1.9.1: Proving the Interior Angle Sum Theorem

  8. Exterior Angle Theorem 1.9.1: Proving the Interior Angle Sum Theorem

  9. Exterior Angle Inequality Theorem 1.9.1: Proving the Interior Angle Sum Theorem

  10. More Theorems 1.9.1: Proving the Interior Angle Sum Theorem

  11. Thanks for Watching! Ms. Dambreville

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