int math 2 section 5-1 1011
Post on 30-Jun-2015
952 Views
Preview:
DESCRIPTION
TRANSCRIPT
Chapter 5Logic and Geometry
created at Wordle.net
Monday, February 6, 2012
Getting to know Geometry
Section 5-1Elements of Geometry
Monday, February 6, 2012
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
Monday, February 6, 2012
Vocabulary1. Geometry:
2. Point:
3. Line:
4. Plane:
5. Space:
Monday, February 6, 2012
Vocabulary1. Geometry: The study of points (and collections of
points) in space
2. Point:
3. Line:
4. Plane:
5. Space:
Monday, February 6, 2012
Vocabulary1. 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:
Monday, February 6, 2012
Vocabulary1. 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:
Monday, February 6, 2012
Vocabulary1. 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:
Monday, February 6, 2012
Vocabulary1. 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 that goes on forever in all directions; has two dimensions (length and width)
5. Space:
Monday, February 6, 2012
Vocabulary1. 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 that goes on forever in all directions; has two dimensions (length and width)
5. Space: The set of all points anywhere and everywhere
Monday, February 6, 2012
More Vocabulary6. Collinear Points:
7. Noncollinear Points:
8. Coplanar Points:
9. Noncoplanar Points:
10. Intersection:
11. Congruent Line Segments:
Monday, February 6, 2012
More Vocabulary6. Collinear Points: Points that lay on the same line
7. Noncollinear Points:
8. Coplanar Points:
9. Noncoplanar Points:
10. Intersection:
11. Congruent Line Segments:
Monday, February 6, 2012
More Vocabulary6. 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:
Monday, February 6, 2012
More Vocabulary6. 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:
Monday, February 6, 2012
More Vocabulary6. 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:
Monday, February 6, 2012
More Vocabulary6. 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:
Monday, February 6, 2012
More Vocabulary6. 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
Monday, February 6, 2012
Even More Vocab12. Midpoint of a Segment:
13. Bisector of a Segment:
14. Postulate:
Monday, February 6, 2012
Even More Vocab12. 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:
Monday, February 6, 2012
Even More Vocab12. 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:
Monday, February 6, 2012
Even More Vocab12. 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
Monday, February 6, 2012
Example 1In the figure, AB and CD bisect each other at point
E. Name congruent segments. D
EAB
C
Monday, February 6, 2012
Example 1In the figure, AB and CD bisect each other at point
E. Name congruent segments. D
EAB
C
AE ≅ EB
Monday, February 6, 2012
Example 1In the figure, AB and CD bisect each other at point
E. Name congruent segments. D
EAB
C
AE ≅ EB CE ≅ ED
Monday, February 6, 2012
Point, Line, and Plane Postulates
Monday, February 6, 2012
Point, Line, and Plane Postulates
Postulate 1: There is exactly one line that goes through any two points
Monday, February 6, 2012
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
Monday, February 6, 2012
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
Monday, February 6, 2012
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
Monday, February 6, 2012
Example 2Refer to the diagram to name the types of points
indicated.
S
R
A
D
G
F
E
H
B
C
Monday, February 6, 2012
Example 2
S
R
A
D
G
F
E
H
B
C
a. Three or more collinear points
Monday, February 6, 2012
Example 2
S
R
A
D
G
F
E
H
B
C
a. Three or more collinear points
A, B, C, D
Monday, February 6, 2012
Example 2
S
R
A
D
G
F
E
H
B
C
b. All points that are coplanar with point F
Monday, February 6, 2012
Example 2
S
R
A
D
G
F
E
H
B
C
b. All points that are coplanar with point F
A, B, C, D, E
Monday, February 6, 2012
Example 2
S
R
A
D
G
F
E
H
B
C
c. All points that are coplanar with E and noncollinear with D
Monday, February 6, 2012
Example 2
S
R
A
D
G
F
E
H
B
C
c. All points that are coplanar with E and noncollinear with D
F
Monday, February 6, 2012
Example 3
S
R
A
D
G
F
E
H
B
C
a. How would you classify the intersection of the two planes?
Monday, February 6, 2012
Example 3
S
R
A
D
G
F
E
H
B
C
a. How would you classify the intersection of the two planes?
The intersection is AD
Monday, February 6, 2012
Example 3
S
R
A
D
G
F
E
H
B
C
a. How would you classify the intersection of the two planes?
The intersection is AD (Postulate 4)
Monday, February 6, 2012
Example 3
S
R
A
D
G
F
E
H
B
C
b. If B and E were to be connected by a line, which plane would they be in?
Monday, February 6, 2012
Example 3
S
R
A
D
G
F
E
H
B
C
b. If B and E were to be connected by a line, which plane would they be in?
The would be in plane S
Monday, February 6, 2012
Example 3
S
R
A
D
G
F
E
H
B
C
b. If B and E were to be connected by a line, which plane would they be in?
The would be in plane S (Postulate 3)
Monday, February 6, 2012
Example 3
S
R
A
D
G
F
E
H
B
C
c. Are F and G able to be connected by a line?
Monday, February 6, 2012
Example 3
S
R
A
D
G
F
E
H
B
C
c. Are F and G able to be connected by a line?
Yes
Monday, February 6, 2012
Example 3
S
R
A
D
G
F
E
H
B
C
c. Are F and G able to be connected by a line?
Yes (Postulate 1)
Monday, February 6, 2012
Problem Set
Monday, February 6, 2012
Problem Set
p. 194 #1-29
“Nothing in life is to be feared. It is only to be understood.” - Marie Curie
Monday, February 6, 2012
top related