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## CHAPTER 3 CHAPTER REVIEW

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**CHAPTER 3**CHAPTER REVIEW**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 m n q**Two lines are skew lines if they do not lie in the same**plane. Skew Lines never intersect. c b ● A**All segments in the diagram**are part of a line and all corners of the cube form right angles. R V 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. Q U W S T X**THEOREMS ABOUT PERPENDICULAR LINES:**GOAL: Use theorems about perpendicular lines Theorem 3.1 Words: All right angles are congruent. A Symbols: If the m A = 90° and m B = 90°, then A B B**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°. 1 4 2 3**Theorem 3.3**Words: If two lines intersect to form adjacent congruent angles, then the lines are perpendicular. ● B A 1 2 ● D ● C Symbols: If 1 2, then AC BD**Theorem 3.4**Words: If two sides of adjacent acute angles are perpendicular, then the angles are complementary. F ● ● G 3 4 ● H ● E Symbols: If EF EH, then m 3 + m 4 = 90°**In the diagram at the right,**EF EH and m GEH = 30 °. Find the value of y. F ● 2y – 12 E ● 30° ● G ● H**Name a pair of alternate interior angles**Name a pair of corresponding angles. Name a pair of same-side interior angles. Name a pair of alternate exterior angles. 1 3 2 4 5 7 6 8**If j ǁ k then find:**m<1 m<2 m<3 m<4 m<5 m<6 m<7 j 72° 1 2 3 k 4 5 6 7**120°**2x + 32 Solve for x.**45°**3x – 15 Solve for x.**74°**5x + 14 Solve for x.**103°**6y – 23 Solve for y.**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.**Examples:**Determine the postulate that proves the lines are parallel. 63° 2. 1. 55° 125° 63°**138°**3. 4. 56° 138° 56° 145° 5. 145°**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. q r s**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. n m p**Determine whether if the given picture is a translation.**2. 1. 3. 4.**PRACTICE**PAGE 160-163 1-32