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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Pair up to check Asg #56, your proof: Prove that the base angles of a proper isosceles trapezoid are equal. Bonus: Prove that a proper trapezoid’s diagonals cannot bisect each other. Warm-up Drawing Exercise

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Pair up to check Asg #56, your proof: • Prove that the base angles of a proper isosceles trapezoid are equal. • Bonus:Provethat a proper trapezoid’s diagonals cannot bisect each other. • Warm-up Drawing Exercise • Lesson: A Triangle Theorem • Homework / Questions • Clean-up

  3. Homework Proof Review • Homework was one or two proofs: • Prove that the base angles of a proper isosceles trapezoid are equal. • Given: Proper isosceles trapezoid ABCD,with legs AD = BC. • Prove: A = B (and C = D). • Hint: Through C, draw CE║DA (by the Parallel Postulate). • Bonus: Prove: A proper trapezoid’s diagonals cannot bisect each other. • Given: Proper trapezoid ABCD with diagonals AC, BD. • Prove: AC and BD do not bisect each other. • Hint: Use an indirect proof.

  4. Warm-up • Draw a trapezoid satisfying these conditions. • Exactly two right angles • At least three right angles • Exactly three equal sides • Equal legs • Equal bases • Which of your trapezoids are proper?

  5. Questions from a Conjecture • How is the area of ABC related to the areaof BDE, DEF, ADF, and FEC? • How is the area of ABC related to the areaof BDE, DEF, ADF, and FEC? • How are DE, DF, and EF related to ABCand its sides?

  6. Simplified • How is DE related to ABC? • How is DE defined?

  7. Midsegments • A midsegment of a triangle is a segment whose endpoints are the midpoints of two sides of the triangle. • DE is a midsegment of ABC.

  8. Midsegment Conjectures • DE║AC ? • DE = AC⁄2? • DE = DA + EC⁄2 ? • AADEC = 3ADBE?

  9. Homework • Hand in Journal #18 today. • 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? • Asg #57: Ch. 7 Algebra Review • Exercises 1-32. • Due Tuesday, 3/12. • Also for Tuesday, 3/12: • Read Ch. 9 Lesson 1 (pp. 338-339), take notes.

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

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