1. CHAPTER 3 CHAPTER REVIEW

2. Relationships Between Lines: GOAL: Identify relationships between lines Two lines are parallel lines if they lie in the same plane and do not intersect. Two lines are perpendicular lines if they intersect to form a right angle. p q n m

3. Two lines are skew lines if they do not lie in the same plane. Skew Lines never intersect. ● c b A

4. X W V U T S R Q Name a line that is skew to VW. Name a plane that appears parallel to plane VWX. Name a line that is perpendicular to plane VWX. All segments in the diagram are part of a line and all corners of the cube form right angles.

5. THEOREMS ABOUT PERPENDICULAR LINES: GOAL: Use theorems about perpendicular lines Theorem 3.1 Words: All right angles are congruent. Symbols: If the m A = 90° and m B = 90°, then A B A B

6. Theorem 3.2 Words: If two lines are perpendicular, then they intersect to form four right angles. Symbols:If n m, then m 1 = 90°, m 2 = 90°, m 3 = 90°, and m 4 = 90°. 4 3 1 2

7. Theorem 3.3 Words:If two lines intersect to form adjacent congruent angles, then the lines are perpendicular. Symbols:If 1 2, then AC BD ●D●D ●B●B ●C●C A 1 2

8. Theorem 3.4 Words: If two sides of adjacent acute angles are perpendicular, then the angles are complementary. Symbols: If EF EH, then m 3 + m 4 = 90° ●H●H ● G F ● ●E●E 3 4

9. In the diagram at the right, EF EH and m GEH = 30 °. Find the value of y. 30° 2y – 12 F ● E ● ●G●G ●H●H

10. 1 2 3 4 5 6 7 8 1.Name a pair of alternate interior angles 2.Name a pair of corresponding angles. 3.Name a pair of same-side interior angles. 4.Name a pair of alternate exterior angles.

11. 72°1 23 45 67 If j ǁ k then find: 1.m<1 2.m<2 3.m<3 4.m<4 5.m<5 6.m<6 7.m<7 j k

12. 120° 2x + 32 Solve for x.

13. 3x – 15 45° Solve for x.

14. 74° 5x + 14 Solve for x.

15. 103° 6y – 23 Solve for y.

16. Showing Lines are Parallel Goal:Show that two lines are parallel. The converse of an if-then statement is the statement formed by switching the hypothesis and the conclusion. Write the converse for the given if-then statement: 1. If two angles have the same measure, then the two angles are congruent.

17. Examples: Determine the postulate that proves the lines are parallel. 1. 63° 2. 55° 125°

18. 3. 138° 56° 145° 5. 4.

19. Theorem 3.11 Words:If two lines are parallel to the same line, then they are parallel to each other. Symbols:If q ǁ r and r ǁ s, then q ǁ s. s q r

20. Theorem 3.12 Words:In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. Symbols:If m p and n p then m ǁ n. p m n

21. Determine whether if the given picture is a translation. 1. 2. 3.4.

22. PRACTICE PAGE 160-163 1-32