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Geometry

Learn how to apply the angle sum theorem, recognize exterior angles, and apply the exterior angle theorem. Understand the vocabulary including exterior angle of a triangle, remote interior angles, and the third angle theorem. Practice with examples and problems included.

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Geometry

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  1. Geometry Notes Section 4-2

  2. What you’ll learn. . . . • How to apply the angle sum theorem • How to recognize exterior angles and apply the exterior angle theorem

  3. Vocabulary • Exterior angle of a triangle • Remote interior angles • Third angle theorem

  4. The Angle Sum Theorem Consider the sum of the angles of a triangle. . . . • The sum of the measures of the angles of a triangle will always be 180°

  5. Example #1:Determine the angle measures.

  6. Example #2:Determine the angle measures.

  7. Example #3:Determine the angle measures

  8. Example #4:Determine the angle measure

  9. The Exterior Angle Theorem 2 4 1 3 Exterior Angles will always make a linear pair with an interior angle of a triangle. • Each exterior angle will be associated with 2 remote interior angles (the two angles not connected to that exterior angle).

  10. The exterior angle theorem: Exterior angles and their remote interior angles share a special relationship. • The measure of an exterior angle of a triangle will always be equal to the sum of the measures of its remote interior angles.

  11. Example Problem #5: • Find x and y.

  12. The Third angle Theorem 2 4 1 5 3 6 If two angles of one triangle measure the same as two angles from another triangle, their third angles must also be the same measure.

  13. Example Problem #6: • Find x and y.

  14. Have you learned. . . . • How to apply the angle sum theorem • How to recognize exterior angles and apply the exterior angle theorem • Assignment: • Non-Proof: Worksheet 4-2 • Proof: p.189 (15-38); all diagrams must be drawn in your homework

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