int math 2 section 5-1 1011

Chapter 5Logic and Geometry

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Monday, February 6, 2012

Getting to know Geometry

Section 5-1Elements of Geometry


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


Vocabulary1. Geometry:

2. Point:

3. Line:

4. Plane:

5. Space:


Vocabulary1. Geometry: The study of points (and collections of

points) in space

2. Point:

3. Line:

4. Plane:

5. Space:



points) in space

2. Point: A location in space that has no dimensions

3. Line:

4. Plane:

5. Space:



points) in space


3. Line: A set of points that goes on forever in both directions; has one dimension (length)

4. Plane:

5. Space:



points) in space



*A line segment is a finite portion of a line

4. Plane:

5. Space:



points) in space




4. Plane: A flat surface that goes on forever in all directions; has two dimensions (length and width)

5. Space:



points) in space




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


More Vocabulary6. Collinear Points:

7. Noncollinear Points:

8. Coplanar Points:

9. Noncoplanar Points:

10. Intersection:

11. Congruent Line Segments:


More Vocabulary6. Collinear Points: Points that lay on the same line

7. Noncollinear Points:

8. Coplanar Points:


10. Intersection:




7. Noncollinear Points: Points not on the same line

8. Coplanar Points:


10. Intersection:





8. Coplanar Points: Points that are all on the same plane


10. Intersection:






9. Noncoplanar Points: Points not on the same plane

10. Intersection:







10. Intersection: The point or points where two things meet (figures, lines, etc.)







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


Even More Vocab12. Midpoint of a Segment:

13. Bisector of a Segment:

14. Postulate:


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:




13. Bisector of a Segment: A line, ray, or segment that goes through the midpoint of another segment

14. Postulate:




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


Example 1In the figure, AB and CD bisect each other at point

E. Name congruent segments. D

EAB

C




EAB

C

AE ≅ EB




EAB

C

AE ≅ EB CE ≅ ED


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 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


Example 2Refer to the diagram to name the types of points

indicated.

S

R

A

D

G

F

E

H

B

C


Example 2

S

R

A

D

G

F

E

H

B

C

a. Three or more collinear points


Example 2

S

R

A

D

G

F

E

H

B

C

a. Three or more collinear points

A, B, C, D


Example 2

S

R

A

D

G

F

E

H

B

C

b. All points that are coplanar with point F


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


Example 2

S

R

A

D

G

F

E

H

B

C

c. All points that are coplanar with E and noncollinear with D


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


Example 3

S

R

A

D

G

F

E

H

B

C

a. How would you classify the intersection of the two planes?


Example 3

S

R

A

D

G

F

E

H

B

C


The intersection is AD


Example 3

S

R

A

D

G

F

E

H

B

C


The intersection is AD (Postulate 4)


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?


Example 3

S

R

A

D

G

F

E

H

B

C


The would be in plane S


Example 3

S

R

A

D

G

F

E

H

B

C


The would be in plane S (Postulate 3)


Example 3

S

R

A

D

G

F

E

H

B

C

c. Are F and G able to be connected by a line?


Example 3

S

R

A

D

G

F

E

H

B

C


Yes


Example 3

S

R

A

D

G

F

E

H

B

C


Yes (Postulate 1)


Problem Set


Problem Set

p. 194 #1-29

“Nothing in life is to be feared. It is only to be understood.” - Marie Curie


int math 2 section 5-1 1011

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