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# Integrated Math 2 Section 5-1

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Elements of Geometry

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### Integrated Math 2 Section 5-1

1. 1. created at Wordle.net Chapter 5 Logic and Geometry
2. 2. Section 5-1 Elements of Geometry G et ti ng to k n o w G eomet ry
3. 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. 4. Vocabulary 1. Geometry: 2. Point: 3. Line: 4. Plane: 5. Space:
5. 5. Vocabulary 1. Geometry: The study of points (and collections of points) in space 2. Point: 3. Line: 4. Plane: 5. Space:
6. 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. 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. 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. 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. 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. 11. More Vocabulary 6. Collinear Points: 7. Noncollinear Points: 8. Coplanar Points: 9. Noncoplanar Points: 10. Intersection: 11. Congruent Line Segments:
12. 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. 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. 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. 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. 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. 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. 18. Even More Vocab 12. Midpoint of a Segment: 13. Bisector of a Segment: 14. Postulate:
19. 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. 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. 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. 22. Example 1 In the figure, AB and CD bisect each other at point E. Name congruent segments. D A E B C
23. 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. 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. 25. Point, Line, and Plane Postulates
26. 26. Point, Line, and Plane Postulates Postulate 1: There is exactly one line that goes through any two points
27. 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. 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. 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. 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. 31. Example 2 a. Three or more collinear points R G D F C B E S A H
32. 32. Example 2 a. Three or more collinear points R G D F C B E S A H A, B, C, D
33. 33. Example 2 b. All points that are coplanar with point F R G D F C B E S A H
34. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 46. Homework
47. 47. Homework p. 194 #1-29 “Nothing in life is to be feared. It is only to be understood.” - Marie Curie