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2.4 & 2.5 Geometry

2.4 & 2.5 Geometry. Brett Solberg AHS ‘11-’12. Warm-up. Solve for x 2(x – 5) = -4 Solve for x. Today’s Objectives. Link reasoning to algebra and geometry. Justify steps of math. No Name Basket/Missing Assignments. Mr. Fix-It. Who is Mr. Fix-It? What tools does he need to do his job?.

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2.4 & 2.5 Geometry

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  1. 2.4 & 2.5 Geometry Brett Solberg AHS ‘11-’12

  2. Warm-up • Solve for x • 2(x – 5) = -4 • Solve for x

  3. Today’s Objectives • Link reasoning to algebra and geometry. • Justify steps of math. • No Name Basket/Missing Assignments

  4. Mr. Fix-It • Who is Mr. Fix-It? • What tools does he need to do his job?

  5. Tools For Math • To reach conclusions we’ll use: • Inductive/Deductive Reasoning • Properties • Postulates • Theorems

  6. Addition Property • If a = b, then a + c = b + c. • Examples • If 2 = 2, then 2 + 4 = 2 + 4. • If x – 2 = 4, then x – 2 + 2 = 4 + 2

  7. Subtraction Property • If a = b, then a – c = b – c. • Examples • If 4 = 4, then 4 – 2 = 4 – 2. • If x + 6 = 10, then x + 6 – 6 = 10 – 6.

  8. Multiplication Property • If a = b, then a*c = b*c • Examples • If 4 = 4, then 4*3 = 4*3 • If x = 3, then *2x = 3*2

  9. Division Property • If a = b and c not equal o, then a/c = b/c. • If 7 = 7, then = . • If 4x = 16, then = .

  10. Distributive Property • a(b + c) = ab + ac • 2(x + 1) = 2x + 2 • x(x – 5) = x2 – 5x

  11. Reflexive Property • a = a • 2 = 2 • ∠a = ∠a

  12. Symmetric Property • If a = b, then b = a. • 4 = 4 • If 2x = 6, then 6 = 2x. • Biconditional

  13. Transitive Property • If a = b and b = c, then a = c. • If angle a = 45, and angle b = 45, then a = b. • Law of Syllogism

  14. Substitution Property • If a = b, then b can replace a. • Angle A and B are complimentary • Angle A = 2x + 1 Angle B = 4x • 2x + 1 +4x = 90

  15. Theorems and Definitions • You can use definitions and theorems to help reach conclusions. • M is the midpoint of AB. • AM congruent to MB by definition.

  16. Using Your Tools • Solve for x • 4x – 2 = 10 • +2 +2 Addition Property • 4x = 12 • /4 /4 Division Property • x = 3

  17. Justify Each Step • Solve For x • ∠CDE & ∠EDF are supplementary • x + (3x + 20) = 180 • 4x + 20 = 180 • 4x = 160 • x = 40 • Angle Addition Post. • Substitution Property • Simplify • Subtraction Property • Division Property

  18. Example 2 Prove x = 6 • AB = 2x, BC = 3x – 9, AC = 21 Given • AB + BC = AC Segment Addition Postulate • 2x + 3x – 9 = 21 Substitution • 5x – 9 = 21 Simplify • 5x – 9 + 9 = 21 + 9 Addition Property • 5x = 30 Simplify • 5x/5 = 30/5 Division Property • x = 6

  19. Theorem • A statement that you prove to be true.

  20. Vertical Angles Theorem • Vertical Angles are Congruent. • ∠1 ≅ ∠3 • ∠2 ≅ ∠4

  21. Given: ∠1 and ∠2, ∠3 and ∠2 are supplementary Prove ∠1 ≅∠3 • ∠1 + ∠ 2 = 180 given • ∠3 + ∠2 = 180 given • ∠1 + ∠2 = ∠2 + ∠3 substitution • ∠1 = ∠3 subtraction

  22. Homework • 2-4 Worksheet • 2-5 pg. 112 #1-13 on back of worksheet

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