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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Lesson: Inequality Postulates & Theorems Homework / Questions Clean-up. G. B. De Savigny The Entertainments of Science , 1905. How does AB compare with BC? (What does that mean?) (What answers are there?) AB > BC AB = BC AB < BC.

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

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

  3. 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

  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. 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.

  6. 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 “”?)

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

  8. 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 “”.) • Multiplication. • If a > b and c > 0, then ac > bc. • Division. • If a > b and c > 0, then a/c > b/c.

  9. Inequality Theorems • Addition of Inequalities (Theorem): • 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.

  10. Homework • Email me (in one message) 5 photos of things with symmetry. Detailed instructions are on the web site. • Due Thursday, 12/20. • Read Chapter 5, Lesson 1, pp. 186-189, and do: • Set I Exercises 5-19. • Set II Exercises 26-31, 41-46, 48. • Bonus: Set III. • Due Thursday, 12/20.

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

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