Understanding Points, Lines, and Planes - Vocabulary & Practice

1. Chapter 1 pt. 1 Understanding Points, Lines, & Planes Vocabulary & Practice

2. y x How to plot points on a coordinate plane? How to simplify expressions and solve equations? Warm – Up: The Coordinate Plane • 1. ** What is the remainder, if you divide by 7. • A. 75  • B. 39  • 2. In a coordinate system, which quadrant is in the lower left-hand portion of the plane? • 3. Points N(5, -2) and M(2, -4) lie on the graph of 2x – 3y = 16. Determine whether P(8, 0) is collinear to N and M. • 4. Graph three points that lie on the graph of y = 4x – 5.

3. How to plot points on a coordinate plane? How to simplify expressions and solve equations? Algebraic Expressions vs. Verbal Expressions • Find Your Match • Sit beside your match.

4. How to simplify expressions and solve equations? What are points, lines, and planes? Algebra 1 Review • Complete “What’s Our Score?”

5. How to simplify expressions and solve equations? What are points, lines, and planes? y x Warm – Up: • 1. Simplify the expression: -y + 3y - 6y + 12y • 2. Solve. 4x – 5 + 3x + 36 = 58 • 3. Plot each point. • 1. A(0, 0) • 2. B(5, 0) • 3. C(-5, 0) • 4. D(0, 5) • 5. E(0, -5) • 6. F(-5, -5)

6. Analyze Your Vocabulary Knowledge • In groups of 2 or 3, determine if you have any knowledge of each term.

7. How to simplify expressions and solve equations? What are points, lines, and planes? Points, Lines, & Planes Pick up: Ruler and Worksheet

8. Sketch and Investigate • Points and Segments • Construct two points and label them “A” and “B.” • Find the distance between the two points. D = ______ • Q1: How can you make the distance between the two points zero?  • Draw a segment connecting the two points. • Measure the length of the segment.  M = ____ • Q2: How does the length of the segment compare to the distance between its endpoints? • Construct a second segment CD with endpoint “D” on the first segment. • Measure the length of segment CD. M = ____ • Q3: How would you find the midpoint of segment CD? • Rays and Lines • Draw a ray with endpoint “J” that passes through a point “K.” Note: a ray extends in one direction. • Q4: Could ray JK also be called ray KJ? Explain. • Q5: Why or Why not can you measure the length of ray JK? • Q6: Why can’t you find the midpoint of a ray? • Draw point M between point J and Point K. • Q7: Give two different names to the ray. R1.__________ R2. ______________  • Construct line XY.  • Q8: Name two rays and a segment that lie on the line. • R1. ________ R2. ________S1.________

9. How to simplify expressions and solve equations? What are points, lines, and planes? (Cont) Sketch and Investigate • Q9: List the similarities and differences between segments, rays, and lines. Complete Venn diagram. Ray Segment Fill in Venn diagram with statements below: Finite Infinitely Long Straight Has 0 endpoints Has 1 endpoints Has 2 endpoints Has a midpoint Line

10. Warm –up: The Real world (chp. 1) • Name a real world example of each and draw a picture. • A. point • B. segment • C. ray • D. line

11. Points, Lines, and Planes Points Lines and Planes Video Review terms from video

12. POINTS • a dot • Represents a specific location in space • Named by one CAPITAL letter • Example: ∙A

13. Infinitely long and straight Has no end points Named by two points on line or one lower case letter Example: Lines

14. COLLINEAR vs NONCOLLINEAR • Collinear: Points that lie on the same line • Example: Points M,A, & N are collinear • Noncolliear: All points do not lie on the same line • Example: Points T, I, & C are noncollinear

15. Has one end point Extends infinitely in one direction Named by its endpoint and a point that it passes through Example: Ray AB Has two endpoints Part of a line or ray Can be measured Named by its endpoints Example: Segment CD RAY SEGMENT

16. PLANE • Flat surface • Extends infinitely in all directions • Name by a single CAPITAL letter or by 3 noncollinear points • Example : Plane KSX or Plane R X K S

17. COPLANAR • Points that lie in the same plane. • Example: Points B, C, D are coplanar • Point A, B, C, D are noncoplanar A F B D C

18. LINES • Parallel Lines: Do not intersect; in the same plane • Intersecting Lines: Lines that meet at a point • Skew Lines: Lines not in the same plane; do not intersect

19. SPACE • A boundless 3-dimensional set of all points

20. PRACTICE

21. Practice: • How many points name a line? • Answer: 2 • How many points name a plane ? • Answer: 3 noncollinear • Draw and label: Line m contains P • Answer: on board

22. Practice: • Are points E, F, and C collinear? • Answer: yes • Are points A, C, D, and E coplanar? • Answer: no • How many planes appear in this figure? • Answer: 5

23. Practice: • Name a point that is not collinear to F and C? • Answer: A, B, D, L, or T • Identify a point that is not in plane N? • Answer: E or F • What is the intersection of plane ADE and plane N? • Answer: Line AD

24. Practice: • Are points A, L, and T collinear? • Answer: no • Are points E, F, and T coplanar? • Answer: yes • Are points B, T, and C collinear? • Answer: yes

25. Draw and label • Ray LK • Line a and line b intersect at C. • line l intersect plane N at X. • Points A, B, C, and D are noncollinear. • Points A, B, C, and D are noncoplanar.

26. State whether each best modeled by a point, line, or plane. • A star in the sky • Answer: point • An ice skating rink • Answer: plane • A telephone wire strung between two poles • Answer: line

27. Individual PracticeHomeworkOpen your textbook to page 9. • worksheet • May work with a partner quietly • Complete problems 1-12, 20,21

28. Warm – Up: Points, Lines, & Planes J H • 1. Are points H, J, K, and L coplanar? • 2. Name three segments that intersect at X. • 3. Are points W, X, Y collinear? • 4. What point(s) do plane WXY and segment WH have in common? L K Z W Y X

29. Quiz: Points, Lines, and Planes • No talking during quiz • When finish, • Pick up a ruler, a marker, and a sheet of patty paper from front table • In textbook, read1.6 (p.43) and 1.2 (p.13)

30. Measuring Segments • Distance • Midpoint

31. Measuring Segments • Locating the Midpoint of a segment • Material: patty paper, ruler, and pencil • ***You can locate the midpoint of any segment by using paper folding • Draw points A and B anywhere on a sheet of patty paper • Connect the points to form segment AB • Fold the paper so that the endpoints A and B lie on top of each other. Pinch the paper to make a crease on the segment. • Open the paper and label the point where the crease intersects segment AB as C. Point C is the midpoint of segment AB.

32. YOUR TURN • Use a ruler to measure segment AC and segment CB. • Repeat the activity with two other segments. • Write a sentence to summarize your observation. • Video: Midpoint and Distance • Groups: Make video tomorrow

33. Warm-up: Measuring Segments • Find a partner • Look around, observe your surroundings, and find a “POINT A” and a “POINT B.” Write it down. • Measure the distance from “POINT A” to “POINT B,” and find the midpoint.

36. Return Quiz • Any questions

37. Locate the place that is midway between Conway & Greenville.

38. Measuring SegmentsGroup Notes &VideoTeach Concept • Distance • Midpoint

39. Make a video explaining how to find the midpoint and distance given a number line or two coordinates. • Resources: Textbook 1.2 p. 13 & 1.6 p.43 and Geometry To Go (bookshelf) • The video must include: • 1. How to find the midpoint of a specified segment on a number line? Explain. Give example. (25pts) • 2. How to find the distance of a specified segment on a number line? Explain. Give example. (25pts) • 3. How to find the midpoint of a segment given two coordinates? Explain. Give example. (25pts) • 4. How to find the distance of a segment given two coordinates? Explain. Give example. (25pts) • 5. Include the following terms correctly in explanations: congruent segments, bisects, and coordinate plane. (bonus)

40. T S V Q W R -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 B Measuring Segments P Given: Number Line Two Coordinate Points Midpoint Formula Distance Formula • Midpoint Formula a + b 2 • Distance Formula | x2 – x1|

41. How to find the midpoint and distance of a segment? Warm-Up # 1 & 2: True or False, and Explain. • 1. The bisector of a segment always intersects the segment at its midpoint. • 2. When 2 lines intersect, a plane is formed. • #3: Use number line D A C B -4 -3 -2 -1 0 1 2 3 4 3. Find the midpoint and distance of segment AB. 4. Find the distance given (-5, 7) & (8, -10)

42. Geometry Textbook Online • http://my.hrw.com/ • Username & Password

43. View Videos • How to find the midpoint and distance given a number line?

44. T S V Q W R -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 B √Measuring Segments P How to find the midpoint and distance of a segment? Given: Number Line Two Coordinate Points Midpoint Formula Distance Formula • Midpoint Formula a + b 2 • Distance Formula | x2 – x1|

45. √ Measuring Segments How to find the midpoint and distance of a segment?

46. How to find the midpoint and distance of a segment? 1.2 Measuring Segments and Constructing Segments TWEET On a Post It Note Think About This p. 16

47. How to find the midpoint and distance of a segment? Segment Addition Postulate between • States: If Q is __________ P and R, then ___________________. • Sketch: • Examples: Given that B is between A and C, find the missing measure. • 1. AB = 6, BC = 4.5, AB_______ • Sketch: PQ + QR = PR

48. How to find the midpoint and distance of a segment? Segment Addition • Example: Given that B is between A and C, find the missing measure. • AC = 15, AB = 6, BC _______ • Sketch: • AB = 2x, BC = 10x, AC= 6, find x. • Sketch:

49. How to find the midpoint and distance of a segment? Practice: Segment Addition

50. Warm-Up: Measuring Segments • 1. Find the distance and midpoint given A(5, -5) & B(-2, 8). • D= • M= • 2. If B is between endpoints A & C, find each missing measure. • A.) If AB = 53 & BC = 21, find AC. • B.) If AB= 13 & BC= 2x , find AC = 3x +7. Find x.