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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Reflection & Planning Lesson: Inequality Postulates & Theorems Homework / Questions Clean-up. 10 minute quick-write. In your journal: Date: January 29, 2014. What do you want to accomplish in 2 nd semester?

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Reflection & Planning • Lesson: Inequality Postulates & Theorems • Homework / Questions • Clean-up

  3. 10 minute quick-write • In your journal: • Date: January 29, 2014. • What do you want to accomplish in 2nd semester? • What do you most want to get better at? • What are some change(s) you want to make, to improve? • What grade do you intend to earn for 2nd semester?

  4. G. B. De SavignyThe Entertainments of Science, 1905 How does AB compare with BC? (What does that mean?) (What answers are there?) AB > BC AB = BC AB < BC

  5. G. B. De SavignyThe Entertainments of Science, 1905 How does AB compare with BC? (What does that mean?) (What answers are there?) AB > BC AB = BC AB < BC

  6. Observation: • There are three possible relationships between two numbers a, b, regarding equality/inequality: • a < b • a = b • a > b • This is the “Three Possibilities” property. • Today’s theme: inequalities.

  7. G. B. De SavignyThe Entertainments of Science, 1905 How do BC and CD compare? AB < BC CD < AB ...so CD < BC. In other words, because “<“ is transitive. (What about “>” and “” and “”?)

  8. Inequalities Solve (verbally – discuss with a neighbor):

  9. Properties of inequality • Three possibilities: a < b, a > b, or a = b. • Transitivity. • Addition. • If a > b, then a + c > b + c. • Subtraction. • If a > b, then a – c > b – c. • (The above also hold for “<”, “”, and “”.)

  10. Properties of inequality • Negative multipliers are special: • Multiplication. • If a > b and c > 0, then ac > bc. • If a > b and c < 0, then ac < bc. • Division. • If a > b and c > 0, then a/c > b/c • If a > b and c < 0, then a/c < b/c

  11. Inequalities What axioms were required?

  12. Inequality Theorems • Addition Theorem of Inequality: • If a > b and c > d,then a + c > b + d. • “The Whole is Greater than the Part” Theorem: • If a > 0, b > 0, and a + b = c,then c > a and c > b. • Pick one and prove it.

  13. Homework • For tonight: • Record the time when you start working. • Work 25 minutes on Asg #39 and/or proving one of the two theorems. (We’ll review #39 on Friday.) • Then take up to 5 minutes to record your work: • Record the stop time. • Which problems did you do? • How difficult (or hard to understand) was it? • Note any hard problem numbers. • Be ready to show me the log & your work tomorrow.

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

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