1. Chapter 3 Review 3.1: Vocabulary and Notation 3.2: Angles Formed by Parallel Lines and Transversals 3.3: Proving Lines are Parallel 3.4: Theorems about Perpendicular Lines

2. Name a pair of vertical angles. 1 2 3 4 5 6 7 8 > >  2 and  3  1 and  4  6 and  8  5 and  7

3. Name a pair of alternate interior angles. 1 2 3 4 5 6 7 8 > >  3 and  7  4 and  8

4. Name a pair of alternate exterior angles. 1 2 3 4 5 6 7 8 > >  2 and  5  1 and  6

5. Name a linear pair of angles. 1 2 3 4 5 6 7 8 > >  1 and  2  2 and  4  3 and  4  1 and  3  7 and  8  7 and  6  5 and  6  5 and  8

6. Name a pair of parallel lines. How do you know they are parallel? Name the transversal. 1 2 3 4 5 6 7 8 > > m n r m || n arrows r

7. Name a pair of corresponding angles. 1 2 3 4 5 6 7 8 > >  2 and  7  1 and  8  3 and  5  4 and  6

8. Describe the relationship between the lines using both words and math notation. x y Perpendicular; x  y

9. Describe the relationship between the lines using both words and math notation. x y > > Parallel; x || y

10. Name a pair of perpendicular segments. P Q R S T U V W

11. Name a pair of skew segments. P Q R S T U V W Examples:

12. Name a pair of parallel segments. P Q R S T U V W

13. Name a pair of parallel planes. P Q R S T U V W

14. Write an equation that describes the relationship between the given angles. State the theorem or postulate that justifies your equation. 1 2 3 4 5 6 7 8 > > m n r Same-side interior angle theorem

15. Write an equation that describes the relationship between the given angles. State the theorem or postulate that justifies your equation. 1 2 3 4 5 6 7 8 > > m n r Corresponding Angles Postulate

16. Write an equation that describes the relationship between the given angles. State the theorem or postulate that justifies your equation. 1 2 3 4 5 6 7 8 > > m n r Linear Pair Theorem

17. Write an equation that describes the relationship between the given angles. State the theorem or postulate that justifies your equation. 1 2 3 4 5 6 7 8 > > m n r Alternate Interior Angles Theorem

18. Write an equation that describes the relationship between the given angles. State the theorem or postulate that justifies your equation. 1 2 3 4 5 6 7 8 > > m n r Alternate Exterior Angles Theorem

19. If  4   6, why is ? 1 2 3 4 5 6 7 8 m n r Converse of the Corresponding Angles Theorem

20. If  3   7, why is ? 1 2 3 4 5 6 7 8 m n r Converse of the alternate interior angles theorem

21. If  2   5, why is ? 1 2 3 4 5 6 7 8 m n r Converse of the alternate exterior angles theorem

22. If  4 and  7 are supplementary, why is ? 1 2 3 4 5 6 7 8 m n r Converse of the same-side interior angles theorem

23. 1 2 3 4 5 6 7 8 m n r Find the value of x that would guarantee m || n.

24. 1 2 3 4 5 6 7 8 m n r

25. What do you know about x? Why? 10 x x>10: The shortest distance between a point not on a line and the line is the segment perpendicular to the segment.

26. What do you know about x? Why? 14

27. Is this a perpendicular bisector? Why or why not? No. We don’t know that the segment has been bisected or the angles formed are right angles– no markings!

28. Is this a perpendicular bisector? Why or why not? No. You can’t bisect a line– only a segment.

29. Is this a perpendicular bisector? Why or why not? Yes. The SEGMENT has been cut in half and the figures intersect at 90 °.

30. Given: h || p Prove:  2   3 StatementsReasons 1. h || p1. Given 2.2. Corresponding angles theorem 3.  1   2 3. 4.  2   3 4. h p 1 2 3  1   3 Vertical angles theorem Transitive Property of 