1 / 22

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?.

karif
Download Presentation

2.4 & 2.5 Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related