1. Lesson 1-5 Postulates and Theorems Relating
Lesson 1-5 Postulates and Theorems Relating Points, Lines, and Planes (page 22)
Essential Question
How are the relationships of geometric figures used in real life situations?

2. __________________ and _____________________.
The phrases, “exactly one” and “one and only one” ⇒
__________________ and _____________________.
existence
uniqueness

3. 2 3 4 Postulate 5 A line contains at least _____ points;
A plane contains at least _____ points not all in one line;
Space contains at least _____ points not all in one plane. 3 4

4. Postulate 6
Through any two points there is exactly
_____ line. 1

5. 1 1 Postulate 7 Through any three points there is at least
_____ plane ;
Through any three noncollinear points
there is exactly _____ plane. 1 1

6. 2 Postulate 8 If _____ points are in a plane, then the line
that contains the points is in that plane.

7. line Postulate 9 If two planes intersect, then their
intersection is a ________.
line

8. THEOREMS: statements that can be ___________.
proved
NOTE:
Writing proofs
will be covered
in Chapter 2.

9. Theorem 1-1 If two lines intersect, then they
intersect in exactly 1 point.
NO PROOF - see classroom exercise #1

10. Theorem 1-2 Through a line and a point not in the
line there is exactly 1 plane.
NO PROOF - see written exercise #20

11. Theorem 1-3 If two lines intersect, then
exactly 1 plane contains the lines.
NO PROOF - see postulate 5 & theorem 1-1

12. Relationships between points …
must
Two points _________ be collinear.
Three points _________ be collinear or noncollinear.
Three points _________ be coplanar.
Three noncollinear points determine a _________.
may
must
plane

13. Relationships between points …
may
Four points _________ be coplanar or noncoplanar.
Four noncoplanar points determine __________.
Space contains at least ____ noncoplanar points.
space 4

14. Three ways to determine a plane …
(1) 3 noncollinear points determine a plane.
Example:

15. Three ways to determine a plane …
A line and a point not on the line determine
a plane.
Example:

16. Three ways to determine a plane …
(3) intersecting lines determine a plane.
Example:

17. Relationships between two lines in the same plane …
intersect
Two lines are either parallel or they _____________
in exactly one point.
Examples:

18. Relationships between a line and a plane …
A line and a plane are either parallel, or
Examples:

19. Relationships between a line and a plane …
A line and a plane are either parallel, or
they _____________ in exactly one point, or
Examples:
intersect

20. Relationships between a line and a plane …
A line and a plane are either parallel, or
they _______________ in exactly one point, or
the plane _______________ the line.
Examples:
intersect
contains

21. Relationships between two planes …
intersect
Two planes are either parallel or they ______________
in a line.
Examples:

27. What is the number of points of intersection for 3 lines?
Draw the relationships to determine your answer.
NO points
1 point
2 points
3 points

28. Written Exercises on pages 25 & 26 RECOMMENDED: 1 to 11 odd numbers
Assignment
Written Exercises on pages 25 & 26
RECOMMENDED: 1 to 11 odd numbers
REQUIRED: 13, 14, 15, 16, 19
How are the relationships of geometric figures used in real life situations?

29. Prepare for a test on Chapter 1 Points, Lines, Planes, and Angles
Assignment
Worksheet on Lesson 1-5
Prepare for a test on Chapter 1
Points, Lines, Planes, and Angles
How are the relationships of geometric figures used in real life situations?