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Lesson 1.1 Patterns and Inductive Reasoning

Lesson 1.1 Patterns and Inductive Reasoning. You will learn to… * find and describe patterns * use inductive reasoning to make conjectures. 8. 4. 14. 16. 2. Sketch the next figure. 1. 2. 5 6 7 6 7 8. __ , __ , __. Describe the pattern. Find the next three numbers.

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Lesson 1.1 Patterns and Inductive Reasoning

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  1. Lesson 1.1Patterns and Inductive Reasoning You will learn to… * find and describe patterns * use inductive reasoning to make conjectures

  2. 8 4 14 16 2 Sketch the next figure. 1. 2.

  3. 5 6 7 6 7 8 __ , __ , __ Describe the pattern. Find the next three numbers. 3. 0, 1, 1, 2, 3, 5, 8,… 13, 21, 34 4. 4, 9, 16, 25, … 36, 49, 64 5. 1 2 3 4 2 3 4 5 __ , __ , __ , __ ,

  4. How many squares are in the next object? 3, 6, 10, 15 6. 1, 4, 9, 16 7.

  5. Architecture

  6. Frank Lloyd Wright

  7. Frank Lloyd Wright Tulip Border Stained Glass Window

  8. A conjecture is an unproven statement that is based on a pattern.

  9. Inductive Reasoning is the process of looking for a pattern and making a conjecture.

  10. Complete the conjecture. 8. The sum of any 2 odd numbers is __________. even 9. The product of any 2 odd numbers is __________. odd

  11. A counterexample is an example that shows a conjecture is false.

  12. Find a counterexample. 10. The sum of 2 numbers is always greater than the larger of the numbers. 11. If a shape has 2 sides the same length, then it must be a rectangle.

  13. Describe the pattern. Find the next numbers or letters in the sequence. 12. J, F, M, A, … M, J, J, A, S, O , N, D O, T, T, F, … 13. F, S, S, E, N, T, … 14. A, 2, B, 0, C, 2, D, 0, E, 3,… F, 3, G, 2, H, 4, …

  14. WorkbookPage 1 (1-5)

  15. Lesson 1.2Points, Lines, and Planes You will learn to… * understand and use the basic geometry terms * sketch intersections of lines and planes

  16. Undefined terms cannot be mathematically defined using other known words. point line plane

  17. Two points determine a line.

  18. B A C Postulate 2 Three points determine a plane. T plane ABC or plane T

  19. A B D C H G E F Do you see… plane ABF ? plane ADG?

  20. C B A C B A Collinear points Coplanar points Coplanar lines points that lie on the same line points that lie in the same plane lines that lie in the same plane

  21. A B C Betweeness refers to collinear points only. Point B is between A and C.

  22. C n B A AB BA CA BC line n Line AB

  23. B A AB BA Segment AB

  24. Is AC the same as AB? B A C NO

  25. B A AB BA Ray AB

  26. B N A NA NB Opposite Rays share an endpoint ? a line Opposite rays form __________.

  27. K J L 1) Draw three noncolinear points J, K, and L.2) Draw JK, KL, and LJ.

  28. If 2 lines intersect, then their intersection is ____________. a point

  29. If 2 planes intersect, then their intersection is ___________. a line

  30. If a line intersects a plane they intersect at __________. a point

  31. Line Designs

  32. WorkbookPage 5 (1-9)

  33. Lesson 1.3Segments & Their Measures You will learn to… * use segment postulates * use the distance formula

  34. The distance between points A and B is written as AB which is the length of AB. A B -3 -2 -1 0 1 2 3 AB = |- 2 – 3| or |3 – - 2| = 5 Distance is the absolute value of their difference.

  35. inches 3 4 6 8 1 1 1. Find the length of the segment. =

  36. inches 1 2 3 8 7 8 1 2 2. Find the length of the segment.

  37. Draw a segment that is…. 3. 4 cm long 4. 2.7 cm long 5. 56 mm long

  38. A postulate is a statement or rule that is accepted without proof. Rules that are proven are called theorems.

  39. AB BC A B C AC Segment Addition Postulate If B is between A and C, then AB + BC = AC.

  40. 20 50 A B C 6. Find AB. AB + 20 = 50 AB = 30

  41. ? A B C 7. Write an expression for AC. 3x + 2 2x - 5 AC = (2x – 5) + (3x + 2) AC = 5x - 3

  42. 8x + 1 12x + 10 A C E 8. Write an expression for AC. AC + (8x + 1) = 12x + 10 AC = 4x + 9

  43. 9. Suppose M is between L and N. Use the Segment Addition Postulate to solve for x. LM = 3x + 8 MN = 2x – 5 LN = 23 L M N 3x + 8 + 2x – 5 = 23 5x + 3 = 23 5x = 20 x = 4

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