1 / 58

Skateboard Sales

Skateboard Sales. About how many skateboards will the shop sell in June? What do you estimate for sales in July? August? Are you comfortable making a guess about next December?. Terminology & Basic Principles. Unit Essential Question:

nibaw
Download Presentation

Skateboard Sales

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. Skateboard Sales • About how many skateboards will the shop sell in June? • What do you estimate for sales in July? August? • Are you comfortable making a guess about next December?

  2. Terminology & Basic Principles Unit Essential Question: How do you identify the basic notations, definitions, properties, and postulates of geometry?

  3. What is Geometry? Geometry

  4. Patterns Essential Question: How do you use inductive reasoning?

  5. Continue the Patterns: • 1, 3, 5, … • 5, 11, 18, 26, … • 1, 4, 9, 16, … • Monday, Tuesday, Wednesday, …

  6. Vocabulary • Inductive Reasoning – Reasoning based on patterns that you observe. • Conjecture – A conclusion you reach based on inductive reasoning. • Counterexample – An example for which the conjecture is incorrect.

  7. Make a Conjecture • What is the sum of the first 30 odd numbers? • (Hint: Look for a pattern)

  8. Conjecture • What is the sum of the first 20 even numbers? • Conjecture: 202

  9. Come up with Counterexamples: • Boys are smarter than girls. • Every prime number is odd. • The square of a number is greater than the number. • You can connect three points to form a triangle. • Every rectangle is a square.

  10. Think, Pair, Share: • What is the goal of using inductive reasoning? • How does inductive reasoning work?

  11. Patterns:

  12. What do you think? • If you have two points, how many lines can you draw through them? • If two lines intersect, what is their intersection? • If two planes intersect, what is their intersection?

  13. Points, Lines, & Planes Essential Questions: What are the basic terms in Geometry?

  14. Points • Point (undefined) – • Name with the capital letter used to label the point.

  15. Lines- • Line (undefined) – Name with any two points on the line, or with a single lower case letter: • AB, n • Collinear – Points that lie on the same line.

  16. Planes • Plane (undefined) – • Plane P, Plane ABC, … • Coplanar – Points that lie on the same plane. • Name the plane for the front of the ice cube, using 3 non-collinear points.

  17. Postulates • Postulate or Axiom – A statement taken as fact. • If you have 2 points, how many lines can you draw through them? • Postulate 1-1: Through any two points there is exactly one line.

  18. Intersection of two lines • If two lines cross, what do they have in common? • Postulate 1-2: If two lines intersect, then their intersection is exactly one point.

  19. Intersection of two Planes • If two planes cross, what is their intersection? • Postulate 1-3: If two planes intersect, then their intersection is exactly one line.

  20. Wobbly chairs • Why do chairs sometimes wobble? • Why doesn’t a tripod wobble? • Postulate 1-4: Three noncollinear points determine exactly one plane. • How many planes contain the same 3 collinear points?

  21. Planes: • Are A, B, G, and H coplanar? If so, shade the plane. • Are B, D, H, and E coplanar? If so, shade the plane. • How many planes contain X, S, and Y? • What is the intersection of Plane VSY and Plane ZYC?

  22. Give an example of: • Two intersecting Lines: • A Line intersecting a Plane: • Two intersecting Planes: • Two planes that do not intersect:

  23. Points, Lines, Planes, & Probability

  24. Textbook Website • Go to: • http://www.phschool.com/math/ • Textbook Companion Sites • Click on High School Math (2007) • Click on Geometry Site • Video Tutorials, Practice Quizzes

  25. Segments, Rays, & Parallel Lines Essential Question: What are segments, rays, and parallel lines?

  26. Vocabulary • Segment – the part of a line consisting of endpoints and the points between them. • Ray – The part of a line consisting of an endpoint and all the points on one side. • Opposite Rays – Two distinct collinear rays with the same endpoint.

  27. Naming Segments & Rays • Name all the segments: • Name all the rays: • Name all the opposite rays:

  28. Lines that do not Intersect • What do you call lines that do not intersect? • Parallel – Coplanar lines that do not intersect. • Skew – Noncoplanar lines. • When are segments and rays parallel or skew? • Parallel Planes – Planes that do not intersect.

  29. Parallel & Skew • Name all segments parallel to GJ. • Name all segments skew to GJ. • Name a line parallel to Plane ABC. • Name a pair of parallel planes.

  30. Think, Pair, Share

  31. Create a Segment • Create a Segment that is 4 Inches long:

  32. Measuring Segments Essential Question: How do you find the length of a segment?

  33. Ruler Postulate • Ruler Postulate – The points of a line can be put into a one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference between their corresponding numbers. • Huh?

  34. Congruence

  35. Example • If A = -3, B = -1, C = 2, D = 4, and E = 5 • Is ? Why or why not? • Compare AB, BC, and AC. What do you see?

  36. Segment Addition Postulate • Why collinear? • Why is B between? • What if there are different letters?

  37. Algebra Example

  38. Midpoint • Where do you think that a midpoint would be located on a segment? • What might make a good definition? • Midpoint – A point on a segment that divides it into two congruent segments. A B

  39. Example

  40. Compare & Contrast Segment Addition Postulate & Midpoints • Similarities • Differences

  41. Word Splash ANGLE

  42. Measuring Angles Essential Question: How do you find the measure of an angle?

  43. What is an Angle? • Angle – Two rays with the same endpoint. • Sides • Vertex

  44. How do you NAME an Angle?

  45. Example • Is it safe to name either angle ?

  46. What does this mean? • Try and create a 73º angle.

  47. Angle Classifications • Acute • Right • Obtuse • Straight

  48. Practice

  49. Congruent Angles • When are Angles Congruent? • Is it the length of their sides? • Is it the angle of their openings?

  50. Angle Addition Postulate

More Related