Lesson 1.2..notebook
August 05, 2016
Before: August 5, 2016
• Anticipation Guide
Agree
Disagree
Statement
Agree
Agree
Disagree
Statement
Agree
Disagree
A point indicates a location and has no size
Disagree
A line is represented by a straight path that extends in two opposite directions without end and has no thickness.
A point indicates a location and has no size.
A line is represented by a straight path that extends in two opposite directions without end and has no thickness.
A line contains a finite amount of points.
A line contains a finite amount of points.
A plane is represented by a non­flat service that extends without end and has a certain thickness to it. A plane is represented by a non­
flat service that extends without end and has a certain thickness to it. A plane contains infinitely many lines.
Points that lie on the same plane are collinear points.
Points and lines that lie in the same plane are coplanar points.
A segment is part of a line that consists of one endpoint and all the points of the line on one side of the endpoint.
A ray is a part of a line that consists of two endpoints and all points between them.
Jul 29­9:37 PM
Agree
Disagree
Statement
Agree
A plane contains infinitely many lines.
Points that lie on the same plane are collinear points.
Jul 29­9:47 PM
Disagree
During: Points, Lines, and Planes
Learning target: I understand basic terms and postulates of geometry.
Points and lines that lie in the same plane are coplanar points.
A segment is part of a line that consists of one endpoint and all the points of the line on one side of the endpoint.
A ray is a part of a line that consists of two endpoints and all points between them.
Jul 29­9:50 PM
AB
Jul 29­9:37 PM
Problem 1: “I Do”
AB
• What are two other ways to name QT?
• What are two other ways to name plane P?
AB
• What are the names of three collinear points? What are the names of four coplanar points?
Aug 4­12:40 PM
Jul 29­9:37 PM
1
Lesson 1.2..notebook
Problem 1: “We Do”
August 05, 2016
B
Problem 1: “You Do”
C
E
• What are two other ways to name RS?
• What are two more ways to name plane P?
• What are the names of three other collinear points?
• What are two points that are NOT coplanar with points R, S, and V?
l
m
A
D
Q
F
• What are two other ways to name AB?
• What are two ways to name plane Q?
• What are the names of three collinear points?
• What are the names of four coplanar points?
Jul 29­9:37 PM
Problem 2: “I Do”
Jul 29­9:37 PM
Problem 2: “You Do”
P
• What are the names of the segments in the figure above?
N
M
• What are the names of the segments in the figure above?
• What are the names of the rays in the figure?
• What are the names of the rays in the figure?
• Which of the rays in part (b) are opposite rays?
• Which of the rays in part (b) are opposite rays? Jul 29­9:37 PM
Jul 29­9:37 PM
Postulate 1­1
•Through any two points there is exactly one line. •Line t passes through points A and B. Line t is the only line that passes through both points. A __________ is an accepted statement of fact. Postulates are basic building blocks of the logical system in geometry. You will use logical reasoning to prove general concepts throughout this semester.
Jul 29­9:37 PM
Jul 29­10:01 PM
2
Lesson 1.2..notebook
August 05, 2016
Postulate 1­2
Postulate 1­3
•If two distinct lines intersect, then they intersect in exactly one point. •If two distinct planes intersect, then they intersect in exactly one line. •AE and DB intersect in point _____. •Plane RST and plane WST intersect in _____. Jul 29­10:05 PM
Jul 29­10:07 PM
Problem 3: “We Do”
Problem 3: “I Do”
• Each surface of the box below represents part of a plane. What is the intersection of plane ADC and plane BFG?
What are the names of two planes that intersect in BF?
Jul 29­9:37 PM
Important!
Jul 29­9:37 PM
Postulate 1­4
•Through any three noncollinear points there is exactly one plane. • When you name a plane from a figure like the box in Problem 3, list the corner points in consecutive order. • For example, plane ADCB and plane ABCD are also names for the plane on the top of the box.
• Plane ACBD is NOT.
Jul 29­9:37 PM
•Points Q, R, and S are non collinear. Plane P is the only plane that contains them.
Jul 29­10:09 PM
3
Lesson 1.2..notebook
Problem 4: “I Do”
Use the figure at the right.
What plane contains points N, P, and Q? Shade the plane.
What plane contains points J, M, and Q? Shade the plane.
Jul 29­9:37 PM
After: Lesson Check
August 05, 2016
Problem 4: “You Do”
Use the figure at the right.
What plane contains points L, M, and N? Copy the figure and shade the plane.
Jul 29­9:37 PM
After: (continued)
• Use the figure at the right.
• What are two other names for XY?
• What are the opposite rays?
• What is the intersection of the two planes?
• A segment has endpoints R and S. What are two names for the segment?
Jul 29­9:37 PM
After: (continued)
• Are AB and BA the same ray? Explain.
Jul 29­9:37 PM
Practice Problems:
• Are AB and BA the same ray? Explain.
• Why do you use two arrowheads when drawing or naming a line such as EF?
• How is naming a ray similar to naming a line? How is it different?
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Page 16, #8 – 14 all and 16 – 24 even
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