WARM UP

1. WARM UP • Factor the following questions. 1. 2. (x+2)(x+2) (3x+2)(x-1) What are points, lines and planes? Can you find examples of these in the real world?

2. Today’s agenda • Quiz over the Alg. Review WS • 1.1 points, lines and planes • The student will be able to: • Define, use correct notation, draw examples and counterexamples of the essential terms for Geometry. • Analyze pictures to solve problem situations.

3. Homework – Algebra review • x=31/17, y=5/34 • x=-1, y=3 • t²+14t+49 • w² - 144 • c² - 4cd + 4d² • x² + 7x + 12 • 2a(5a + 2) • 5ab²(5a + 6b) • -25. on board • 48 • 238 • 6(2a+b) • 11.8a+8.8b • v=3 • null set • m=-5 • y=3 • x=3, y=9 • y=2, x=2 • Real life: • 127.28 ft • 26.93 ft • 10.63 ft • 7.21 ft • YES (19.21 in.) Quiz time!

4. Unit 1 Ch.1 Points, Lines and Planes

5. Think of a football, volleyball, band, etc. . . . • What terms do you use? • How do you learn them? • Does it make sense when you first learn something new?

6. Vocabulary Undefined term Defined terms A word without a formal definition In geometry, point, line, plane are undefined Terms that can be described using known words

7. Point: has no dimension. Line: has one dimension and extends without end. 1. How we name points

8. 1. How we name points . . .

9. Taking notes will help!Defined terms: ______________ AB, or segment AB, written as _____ consists of the ________ A and B and all points on AB that lie between A and B. Line segment endpoints AB A B This segment has two names!

10. Taking notes will help! Ray AB consists of the endpoint A and all the points on line AB that lie on the same side of A as B. AB A B note ray BA is a different ray! Opposite ray

11. 2. How we name lines . . . HF, FH

12. 4. How we name planes K Plane AGC, Plane EDI, Plane K…

13. Vocabulary Collinear points Coplanar points Intersection Between Points that lie on the same line Points that are in the same plane The set of points that two or more figures have in common When three points are collinear, you can say that one point is between the other two.

14. Angle: consists of two different rays with the same endpoint. The rays are the sides of the angle and the endpoint is the vertex of the angle. Vertex: endpoint where two different segments or rays connect 3. How we name angles <GBC, <CBG

15. Point Line Plane you are asked to accept them Undefined terms A D B C H

16. a. Give two other names for PQand for plane R. point V Line PT b. Name three points that are collinear. c. Where do plane R and line QV intersect? d. Where do plane R and plane QPT intersect? PQ akaQPand line n. plane R or plane SVT or plane PTV. EXAMPLES Name points, lines, and planes S, P, and Tlie on the same line.

17. Terms you need to know • In your notes • Be sure to have the term, the definition, the notation and an example, I usually give extra examples. • Write your notes so you understand them . . . They are not for my benefit, but yours! • After each example be sure you understand the example (s) we covered . . . If you don’t, please ask – I doubt you are the only one . . . You are smart enough to ask! • Use tutoring when needed . . . Don’t wait until you are totally lost . . . Everything builds . . . A few minutes help may clear up your confusion. • Keep up with your definitions and “For your notebook”

18. Parallel lines: two lines that do not intersect and are coplanar. • Skew lines: two lines that do not intersect and are not coplanar. • Perpendicular lines: two lines that intersect and form a right angle.

19. G E F J H • a. Give another name for GH • b. Name all rays with endpoint J. Which of these rays are opposite rays? • c. Give another name for EF. • d. Are HJ and JH the same ray? Are HJ and HG the same ray? Explain. • e. Sketch a plane and a line that is in the plane. • f. Sketch a plane and a line that doesn’t intersect the plane. • g. Sketch a plane and a line that intersects the plane at a point.

20. a. Name the intersection of PQ and line k. • b. Name the intersection of plane A and plane B. • c. Name the intersection of line k and plane A.

21. Are points R, K, L collinear? Coplanar? • Are points E,L collinear? • Are points R,H and G coplanar? • Are points M, J collinear? • Are points M, G and J coplanar? • Name a pair of skew lines. • Name a pair of parallel lines. • Name a pair of perpendicular lines.

22. Are points X ,Y collinear? • Choose the correct name for the plane: • XWQ, ZWY or ZWQ. • What does the P on the picture represent? • What does the m represent?

23. Collinear & Coplanar

24. H I L B Are M, G, and H collinear? NO D M G C E K A J F

25. H I L B D YES M G C E Are B, G, and K collinear? K A J F

26. H I L B D M G C E A K Are B, G, K and J collinear? NO J F

27. B C D A F G E H Identify which plane contains the points A, B, and D. Plane ABD, or Plane ABC, or plane CDB or plane ACD or … . . . .

28. Here’s the plane through A, B, and D! Is H in it also? B C D A F G E H Are points A, B, D, and H coplanar? NO

29. Intersections • Two or more geometric shapes intersect if they have one or more points in common. Two lines that do not intersect are either parallel lines or skew lines. Two lines are parallel lines if they do not intersect and are coplanar. Two lines are skew lines if they do not intersect and are not coplanar.

30. B C D A F G E H Are AE and FG skew? Yes!

31. B C D A F G E H Are AD and FG skew? NO!

32. Know the difference • Line segment • Line • Ray • Distance • collinear • opposite rays

33. Think of a football field or a volleyball court – when viewed from a coaches clipboard . . . • People – points • Yard lines/ out of bounds – lines • The field/court - plane

34. What are some real world examples of . . .in the classroom and outside . . . • Planes • Lines • Points

35. EVALUATION • In class practice • Complete the worksheet 1.1 AWESOME JOB!!!!