This document provides an overview of fundamental geometric concepts. It begins by defining geometry as the study of points and collections of points in space. Key terms are introduced such as point, line, plane, and space. Properties of these concepts like collinear points, coplanar points, and intersections are explained. Examples are provided to demonstrate classifying types of points and intersections. The document concludes by presenting postulates about points, lines, and planes that are assumed to be true in geometry. For homework, problems 1-29 on page 194 are assigned.

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Chapter 5
Logic and Geometry

2. Section 5-1
Elements of Geometry
G et ti ng to k n o w G eomet ry

3. Essential Questions
What are the fundamental geometric concepts?
What are the basic geometric postulates and how
do you use them?
Where you’ll see this:
Construction, art, photography, navigation

4. Vocabulary
1. Geometry:
2. Point:
3. Line:
4. Plane:
5. Space:

5. Vocabulary
1. Geometry: The study of points (and collections of
points) in space
2. Point:
3. Line:
4. Plane:
5. Space:

6. Vocabulary
1. Geometry: The study of points (and collections of
points) in space
2. Point: A location in space that has no dimensions
3. Line:
4. Plane:
5. Space:

7. Vocabulary
1. Geometry: The study of points (and collections of
points) in space
2. Point: A location in space that has no dimensions
3. Line: A set of points that goes on forever in both
directions; has one dimension (length)
4. Plane:
5. Space:

8. Vocabulary
1. Geometry: The study of points (and collections of
points) in space
2. Point: A location in space that has no dimensions
3. Line: A set of points that goes on forever in both
directions; has one dimension (length)
*A line segment is a finite portion of a line
4. Plane:
5. Space:

9. Vocabulary
1. Geometry: The study of points (and collections of
points) in space
2. Point: A location in space that has no dimensions
3. Line: A set of points that goes on forever in both
directions; has one dimension (length)
*A line segment is a finite portion of a line
4. Plane: A flat surface the goes on forever in all
directions; has two dimensions (length and width)
5. Space:

10. Vocabulary
1. Geometry: The study of points (and collections of
points) in space
2. Point: A location in space that has no dimensions
3. Line: A set of points that goes on forever in both
directions; has one dimension (length)
*A line segment is a finite portion of a line
4. Plane: A flat surface the goes on forever in all
directions; has two dimensions (length and width)
5. Space: The set of all points anywhere and
everywhere

11. More Vocabulary
6. Collinear Points:
7. Noncollinear Points:
8. Coplanar Points:
9. Noncoplanar Points:
10. Intersection:
11. Congruent Line Segments:

12. More Vocabulary
6. Collinear Points: Points that lay on the same line
7. Noncollinear Points:
8. Coplanar Points:
9. Noncoplanar Points:
10. Intersection:
11. Congruent Line Segments:

13. More Vocabulary
6. Collinear Points: Points that lay on the same line
7. Noncollinear Points: Points not on the same line
8. Coplanar Points:
9. Noncoplanar Points:
10. Intersection:
11. Congruent Line Segments:

14. More Vocabulary
6. Collinear Points: Points that lay on the same line
7. Noncollinear Points: Points not on the same line
8. Coplanar Points: Points that are all on the same
plane
9. Noncoplanar Points:
10. Intersection:
11. Congruent Line Segments:

15. More Vocabulary
6. Collinear Points: Points that lay on the same line
7. Noncollinear Points: Points not on the same line
8. Coplanar Points: Points that are all on the same
plane
9. Noncoplanar Points: Points not on the same plane
10. Intersection:
11. Congruent Line Segments:

16. More Vocabulary
6. Collinear Points: Points that lay on the same line
7. Noncollinear Points: Points not on the same line
8. Coplanar Points: Points that are all on the same
plane
9. Noncoplanar Points: Points not on the same plane
10. Intersection: The point or points where two things
meet (figures, lines, etc.)
11. Congruent Line Segments:

17. More Vocabulary
6. Collinear Points: Points that lay on the same line
7. Noncollinear Points: Points not on the same line
8. Coplanar Points: Points that are all on the same
plane
9. Noncoplanar Points: Points not on the same plane
10. Intersection: The point or points where two things
meet (figures, lines, etc.)
11. Congruent Line Segments: Two or more line
segments that have the same length

18. Even More Vocab
12. Midpoint of a Segment:
13. Bisector of a Segment:
14. Postulate:

19. Even More Vocab
12. Midpoint of a Segment: The point that divides the
line segment into two equal line segments (It’s in
the middle!)
13. Bisector of a Segment:
14. Postulate:

20. Even More Vocab
12. Midpoint of a Segment: The point that divides the
line segment into two equal line segments (It’s in
the middle!)
13. Bisector of a Segment: A line, ray, or segment that
goes through the midpoint of another segment
14. Postulate:

21. Even More Vocab
12. Midpoint of a Segment: The point that divides the
line segment into two equal line segments (It’s in
the middle!)
13. Bisector of a Segment: A line, ray, or segment that
goes through the midpoint of another segment
14. Postulate: A rule in geometry that is assumed to
be true

22. Example 1
In the figure, AB and CD bisect each other at point
E. Name congruent segments.
D
A E
B
C

23. Example 1
In the figure, AB and CD bisect each other at point
E. Name congruent segments.
D
A E
B
C
AE ≅ EB

24. Example 1
In the figure, AB and CD bisect each other at point
E. Name congruent segments.
D
A E
B
C
AE ≅ EB CE ≅ ED

25. Point, Line, and Plane
Postulates

26. Point, Line, and Plane
Postulates
Postulate 1: There is exactly one line that goes
through any two points

27. Point, Line, and Plane
Postulates
Postulate 1: There is exactly one line that goes
through any two points
Postulate 2: There is exactly one plane that goes
through any three noncollinear points

28. Point, Line, and Plane
Postulates
Postulate 1: There is exactly one line that goes
through any two points
Postulate 2: There is exactly one plane that goes
through any three noncollinear points
Postulate 3: The line connecting any two points
on a plane also lies in that same plane

29. Point, Line, and Plane
Postulates
Postulate 1: There is exactly one line that goes
through any two points
Postulate 2: There is exactly one plane that goes
through any three noncollinear points
Postulate 3: The line connecting any two points
on a plane also lies in that same plane
Postulate 4: The intersection of any two planes is
a line

30. Example 2
Refer to the diagram to name the types of points
indicated.
R
G
D
F
C
B
E
S
A
H

31. Example 2
a. Three or more collinear points
R
G
D
F
C
B
E
S
A
H

32. Example 2
a. Three or more collinear points
R
G
D
F
C
B
E
S
A
H
A, B, C, D

33. Example 2
b. All points that are coplanar with point F
R
G
D
F
C
B
E
S
A
H

34. Example 2
b. All points that are coplanar with point F
R
G
D
F
C
B
E
S
A
H
A, B, C, D, E

35. Example 2
c. All points that are coplanar with E and
noncollinear with D
R
G
D
F
C
B
E
S
A
H

36. Example 2
c. All points that are coplanar with E and
noncollinear with D
R
G
D
F
C
B
E
S
A
H
F

37. Example 3
a. How would you classify the intersection of the
two planes?
R
G
D
F
C
B
E
S
A
H

38. Example 3
a. How would you classify the intersection of the
two planes?
R
G
D
F
C
B
E
S
A
H
The intersection is AD

39. Example 3
a. How would you classify the intersection of the
two planes?
R
G
D
F
C
B
E
S
A
H
The intersection is AD (Postulate 4)

40. Example 3
b. If B and E were to be connected by a line, which
plane would they be in?
R
G
D
F
C
B
E
S
A
H

41. Example 3
b. If B and E were to be connected by a line, which
plane would they be in?
R
G
D
F
C
B
E
S
A
H
The would be in plane S

42. Example 3
b. If B and E were to be connected by a line, which
plane would they be in?
R
G
D
F
C
B
E
S
A
H
The would be in plane S (Postulate 3)

43. Example 3
c. Are F and G able to be connected by a line?
R
G
D
F
C
B
E
S
A
H

44. Example 3
c. Are F and G able to be connected by a line?
R
G
D
F
C
B
E
S
A
H
Yes

45. Example 3
c. Are F and G able to be connected by a line?
R
G
D
F
C
B
E
S
A
H
Yes (Postulate 1)

46. Homework

47. Homework
p. 194 #1-29
“Nothing in life is to be feared. It is only to be
understood.” - Marie Curie