1. Lesson 1.6
Incidence Theorems pp

2. Objectives:
1. To prove some incidence theorems from the Incidence Postulates.

3. Theorem 1.1
If two distinct lines intersect, they intersect in one and only one point.

4. If two lines intersect, how many points of intersection are there?

5. Consider the diagram. A B C
How many lines pass through both A and B?

6. Consider the diagram. A B C
How many planes pass
through AB?

7. Consider the diagram. A B C
How many planes can pass through A, B, and C?

8. Consider the diagram. A B C
How many planes pass through any three given noncollinear points?

9. Consider the diagram. A B C
How many planes pass
through point C and AB?

10. Theorem 1.2
A line and a point not on that line are contained in one and only one plane.

11. Theorem 1.3
Two intersecting lines are contained in one and only one plane.

12. Consider these lines:

13. Theorem 1.4
Two parallel lines are contained in one and only one plane.

14. Consider these lines:

15. Homework pp

16. ►A. Exercises
Answer each question, explain your answer, and state a definition, postulate, or theorem that supports your answer.
1. Does AB lie in plane m? m A C D B E

17. ►A. Exercises
Answer each question, explain your answer, and state a definition, postulate, or theorem that supports your answer.
3. How many planes pass through points A, E, and D? m A C D B E

18. ►A. Exercises
Answer each question, explain your answer, and state a definition, postulate, or theorem that supports your answer.
5. How many planes pass through
CD and point E? m A C D B E

19. ►A. Exercises
Answer each question, explain your answer, and state a definition, postulate, or theorem that supports your answer.
7. What is the intersection of ED and
DB? m A C D B E

20. ►A. Exercises
Answer each question, explain your answer, and state a definition, postulate, or theorem that supports your answer.
7. Is there more than one point of intersection? m A C D B E

21. ►A. Exercises
Answer each question, explain your answer, and state a definition, postulate, or theorem that supports your answer.
9. If AD is parallel to CB, will these two lines ever intersect? m A C D B E

22. 11. A line and a point not on that line
►B. Exercises
11. A line and a point not on that line
are contained in one and only one
plane. B A C D H E G F

23. 13. Two parallel lines are contained in one and only one plane.
►B. Exercises
13. Two parallel lines are contained in one and only one plane. B A C D H E G F

24. 15. If two lines intersect, then the lines
►B. Exercises
15. If two lines intersect, then the lines
are contained in one and only one
plane. B A C D H E G F

25. ►B. Exercises
17. Are BC and EF skew lines? B A C D H E G F

26. ►B. Exercises
19. Give the reasoning behind this
statement: “There are at least three
lines in any plane.”

27. ■ Cumulative Review
27. Name three undefined terms.

28. ■ Cumulative Review
28. Name three defined terms.

29. ■ Cumulative Review
29. Name a postulate.

30. ■ Cumulative Review
30. State a theorem.

31. ■ Cumulative Review 31. According to the postulates and
theorems so far, must there be an
infinite number of points in space?
Explain.