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Section 1-2: Points, Lines, and Planes. Goal 2.02: Apply properties, definitions, and theorems of angles and lines to solve problems. Essential Questions. 1.) How do you identify and model points, lines, and planes?

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section 1 2 points lines and planes

Section 1-2: Points, Lines, and Planes

Goal 2.02: Apply properties, definitions, and theorems of angles and lines to solve problems

essential questions
Essential Questions
  • 1.) How do you identify and model points, lines, and planes?
  • 2.) How are coplanar points, intersecting lines, and planes identified?
  • 3.) How are the basic postulates and theorems about points, lines, and planes used?
section 1 1 homework
Section 1-1 Homework
  • P 7 (25- 39)
  • 25 – 28) answers vary
  • 29.) 75 30) 40
  • 31.) 31, 43 32.) 10, 13
  • 33.) .0001, .00001 34.) 201, 202
  • 35.) 63, 127 36.) 31/32, 63/64
  • 37.) J, S 38) CA, CO 39) B, C
three undefined terms
Three Undefined Terms
  • Point
  • Line
  • Plane
space
space
  • the set of all points
collinear points
collinear points
  • points all in one line
coplanar points
coplanar points
  • points all in one plane
intersection of two figures
intersection of two figures
  • the set of points that are in both figures
postulates or axioms
postulates (or axioms)
  • statements accepted without proof
theorems
theorems

statements that have been proven

5 basic postulates
5 Basic Postulates
  • 1.) A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane.
  • 2.) Through any two points there is exactly one line.
  • 3.) Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.
  • 4.) If two points are in a plane, then the line that contains is in that plane.
  • 5.) If two planes intersect, then intersection is a line.
3 basic theorems
3 Basic Theorems
  • 1.) If two lines intersect, then they intersect in exactly one point.
  • 2.) Through a line and a point not in the line there is exactly one plane.
  • 3.) If two lines intersect, then exactly one plane contains the line.
examples p 13 1 9 odd
Examples, p 13 (1-9 odd)
  • 1.) A, D, E 3.) B, C, F
  • 5.) F, B, D 7.) G, F, C
  • 9.) Name line m in three other ways.
  • Do p 13 (2-10 even)
p 14 11 43 odds
P 14 (11 - 43 odds)

11.) the bottom 13.) the front

15.) the left side 17.) Planes QRS and RSW

19.) Planes XWV and UVR

21.) QU 23.) XT

25.) R, V, W 27.) U, X, S

29.) T, V, R 31.) plane UVW

33.) plane TUX 35.) point Q with V, W, S

37.) point W with X, V, R 39.) S, U, V, Y

41.) X, S, V, U 43.) S, V, C, Y

slide15

With partners p 14 (12 – 42 even)

  • Discuss always, sometimes or never questions
  • Review counterexample
  • Together p 15 (60 – 65 all)
  • Independent Practice: p 16 (85-89 all)
homework
Homework
  • Textbook: p 9 (56 – 59 all)
  • Workbook: Practice 1-2