3.3 prove lines are parallel

3.3 prove lines are parallel

• 1.
  3.33.3 Prove Linesare Parallel Bell Thinger 2. Write the converse of the following statement. If it is raining, then Josh needs an umbrella. ANSWER If Josh needs an umbrella, then it is raining. ANSWER 32 1. Find the value of x.
• 2.
  3.3
• 3.
  3.3Example 1 ALGEBRA Find thevalue of x that makes m n. SOLUTION Lines m and n are parallel if the marked corresponding angles are congruent. 3x = 60 x = 20 The lines m and n are parallel when x = 20. (3x + 5) o = 65o Use Postulate 16 to write an equation Subtract 5 from each side. Divide each side by 3.
• 4.
  3.3Guided Practice 1. Isthere enough information in the diagram to conclude that m n? Explain. ANSWER Yes. m n because the angle corresponding to the angle measuring 75 o also measures 75 o since it forms a linear pair with the 105o angle. So, corresponding angles are congruent and Postulate 16 says the lines are parallel.
• 5.
  3.3
• 6.
  3.3Example 2 How canyou tell whether the sides of the pattern are parallel in the photo of a diamond- back snake? Snake Patterns SOLUTION Because the alternate interior angles are congruent, you know that the sides of the pattern are parallel.
• 7.
  3.3Guided Practice Can youprove that lines a and b are parallel? Explain why or why not. 3. Yes; Alternate Exterior Angles Converse ANSWER
• 8.
  3.3Guided Practice Can youprove that lines a and b are parallel? Explain why or why not. Yes; Corresponding Angles Converse ANSWER 4.
• 9.
  3.3Guided Practice Can youprove that lines a and b are parallel? Explain why or why not. No; Supplementary angles do not have to be congruent. ANSWER 5. m 1 + m 2 = 180°
• 10.
  3.3Example 3 Prove thatif two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. SOLUTION GIVEN : 4 5 PROVE : g h
• 11.
  3.3Example 3 g h4.4. Corresponding Angles Converse STATEMENTS REASONS 1. Given1. 4 5 2. 1 4 2. Vertical Angles Congruence Theorem 3. 1 5 3. Transitive Property of Congruence
• 12.
  3.3
• 13.
  3.3Example 4 SOLUTION Look atthe diagram to make a plan. The diagram suggests that you look at angles 1, 2, and 3. Also, you may find it helpful to focus on one pair of lines and one transversal at a time. In the figure, r s and 1 is congruent to 3. Prove p q.
• 14.
  3.3Example 4 Plan forProof a. Look at 1 and 2. Look at 2 and 3.b. 1 2 because r s. If 2 3 then p q.
• 15.
  3.3Example 4 Plan inAction a. It is given that r s, so by the Corresponding Angles Postulate, 1 2. b. It is also given that 1 3. Then 2 3 by the Transitive Property of Congruence for angles. Therefore, by the Alternate Interior Angles Converse, p q.
• 16.
  3.3
• 17.
  3.3Example 5 The flagof the United States has 13 alternating red and white stripes. Each stripe is parallel to the stripe immediately below it. Explain why the top stripe is parallel to the bottom stripe. U.S. Flag SOLUTION The stripes from top to bottom can be named s1, s2, s3, . . . , s13. Each stripe is parallel to the one below it, so s1 s2, s2 s3, and so on. Then s1 s3 by the Transitive Property of Parallel Lines. Similarly, because s3 s4, it follows that s1 s4. By continuing this reasoning, s1 s13. So, the top stripe is parallel to the bottom stripe.
• 18.
  3.3 8. Each stepis parallel to the step immediately above it. The bottom step is parallel to the ground. Explain why the top step is parallel to the ground. ANSWER All of the steps are parallel. Since the bottom step is parallel to the ground, the Transitive Property of Parallel Lines applies, and the top step is parallel to the ground. Guided Practice
• 19.
  3.3Exit Slip 1. Findthe value of x that makes p q. 43ANSWER Can you prove a b? If so, what theorem would you use? 2. Yes; Alternate Interior Angle ConverseANSWER
• 20.
  3.3Exit Slip 3. Whichlines are parallel? EF DGANSWER 4. In the figure, if HJ KL and KL MN, what can you conclude? What theorem justifies your conclusion? HJ MN by Transitive Property of Parallel Lines ANSWER
• 21.
  3.3 Homework Pg 169-173 #8, 14,19, 29, 33