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GBK Geometry

GBK Geometry. Jordan Johnson. Today’s plan. Greeting Warm-up: Practice Quiz Lesson: Similarity Practice Work Lesson: The Side-Splitter Theorem Return Unit 9 Tests Homework / Questions Clean-up. Not a Quiz. Half-sheet, name & date (5/8 or 5/9) at top right. Title: Not-a-quiz: Means

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GBK Geometry

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  1. GBK Geometry Jordan Johnson

  2. Today’s plan • Greeting • Warm-up: Practice Quiz • Lesson: Similarity • Practice Work • Lesson: The Side-Splitter Theorem • Return Unit 9 Tests • Homework / Questions • Clean-up

  3. Not a Quiz • Half-sheet, name & date (5/8 or 5/9) at top right. • Title: Not-a-quiz: Means • Find the exact arithmetic and geometric means of • 4 and 6 • 25 and 49 • 10 and 100 • Check that your answer is plausible.

  4. Similarity: Definition • Two triangles are similar iff there is a correspondence between their vertices such that • corresponding angles are equal • corresponding sides are proportional • Iff ΔABC ~ ΔEFG, then: • A = E, B = F, C = G • and AB⁄EF = BC⁄FG = AC⁄EG

  5. Similarity: Alternate Definition • Two triangles are similar iff one is the dilation image of the other.

  6. Goals • Your immediate goals: • Solve proportions quickly so you can relate one shape’s size to another’s. • Recognize when shapes are similar. • Write the equations that describe similarity. • Our longer-term goal: • Develop ways to prove shapes are similar. • Triangles first, then other shapes.

  7. Problems • In groups of two or three, complete: • Ch. 10 Lesson 2, Exercises 48-51. (Page 391.)

  8. Problems • In groups of two or three, complete: • Ch. 10 Lesson 2, Exercises 48-51. (Page 391.) • What numbers have 4 as their geometric mean? • What numbers have 12 as their geometric mean? • Come up with (and write down) a procedure for finding numbers that have a given geometric mean.

  9. Theorem • The Side-Splitter Theorem (Theorem 44): • If a line parallel to one side of a triangle intersects the other two sides in different points, then it divides the sides in the same ratio. • Given: (with D on AB and E on AC) • Prove:

  10. Proof H I

  11. Corollary (p. 394) • If a line parallel to one side of a triangle intersects the other two sides in different points, it creates segments proportional to those sides. • Given:ABC, and line DE║BC, with D and E lying on AB and AC. • Prove:AD⁄AB = AE⁄AC and DB⁄AB = EC⁄AC

  12. Work • Now: • Week 33 Journal • Asgs #67-70 • 50+ minutes over the weekend: • Read pp. 392-394 and review the proof. • Work on any of Asgs #67 - #70. • Unit 9 Test Analysis

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

  14. Mini-Quiz • Half-sheet of paper; name/date at top-right. • Title: Mini-Quiz, Similarity / Geo. Mean. • Fill in the blanks in the following: • In two similar figures… • …corresponding segments are _____________________. • …corresponding angles are ____________________. • “ABC  XYZ” means “_________________________.” • If ABC  XYZ, we can say AB⁄XY = ___ ⁄___ = ___ ⁄___and also A = ___, B = ___, and C = ___. • Similarity is relation by a _____________, just as congruence is relation by an isometry. • Find the exact geometric mean of 6 and 18.

  15. Problems • In groups of two or three, complete: • Ch. 10 Lesson 2, Exercises 48-51. (Page 391.) • What numbers have 4 as their geometric mean? • What numbers have 12 as their geometric mean? • Come up with (and write down) a procedure for finding numbers that have a given geometric mean.

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