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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan – Proof Practice. Greeting Warm-up Proof Triangle Angle Sum Theorem A Practical Proof Homework / Questions Clean-up. Prove – In Pairs. Definition:

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan – Proof Practice • Greeting • Warm-up Proof • Triangle Angle Sum Theorem • A Practical Proof • Homework / Questions • Clean-up

  3. Prove – In Pairs • Definition: • Two angles formed by a transversal are alternate exterior angles iff they lie outside of the two lines traversed and are on opposite sides of the transversal. • Prove: • Alternate exterior angles on parallel lines are equal.

  4. Theorem 20 • The Triangle Angle-Sum Theorem: • The sum of the angles of a triangle is 180°. • Given: ABC. • Prove: A + B + C = 180°. • Beginning: • Construct line DE, parallel to AC and passing through B. • (What rule permits this?) • Pair up and prove it.

  5. Corollaries to theTriangle Angle-Sum Theorem • If two angles of one triangle are equal to two angles of another triangle, then the third pair of angles are equal. • The acute angles of a right triangle are complementary. • Each angle of an equilateral triangle is 60°.

  6. Going further... • Triangle Angle-Sum Theorem Strong Exterior Angle Theorem • Theorem 21: The StrongExterior Angle Theorem: • An exterior angle of a triangle is equal to the sum of the remote interior angles. • This is “strong” because it makes a statement that implies the “weak” theorem and more.

  7. What are these?

  8. A MiterGauge • Set to the angle desired for the cut. • Push along a slot parallel to the blade.

  9. A MiterGauge • Sketch a diagram and use it to prove that the angle of the cut will equal the angle of the gauge.

  10. Work • Finish Journal #15: • What did you do here? How did you use your time? What did you learn? • Were there any surprises this week? (Meaning, any events or solutions or discoveries you found surprising?) • What words / concepts were new to you this week? What do they mean? • What was good about this week’s classes for you? • What can you and I do better next week? • Do you have any other comments? • Due Thursday (per. 1-3) or Friday (per. 7). • Asg #50: Read Ch. 6 Lesson 5 (pp. 238-241) and do: • Set I Exercises 1-18. • Set II Exercises 31-45. • Bonus: Set III. • Due Monday, 2/11.

  11. Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!

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