Elements of Geometry

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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