1. Lesson 3-5 Menu 1.Write an equation in point-slope form of a line having slope as ¾ and contains the point (5, –2). 2.Write an equation in point-slope form of a line having slope as 3 and contains the point (–2, 7). 3.Write an equation in slope-intercept form of a line having slope as –3 and contains the point (0, 2.5). 4.Write an equation in slope-intercept form of a line having slope as –½ and contains the point (4, –6). 5.Write an equation in slope-intercept form of a line passing through (1, 5) and (3, 11).

2. Lesson 3-5 Ideas/Vocabulary Recognize angle conditions that occur with parallel lines. Prove that two lines are parallel based on given angle relationships.

3. Lesson 3-5 Postulates

4. Lesson 3-5 Theorems

5. Since RQT and SQP are vertical angles, m SQP = 77. Lesson 3-5 Example 1 Determine which lines, if any, are parallel. Identify Parallel Lines Since m UPQ + m SQP = 103 + 77 or 180, consecutive interior angles are supplementary. So, a || b. Since m TQR + m VRQ = 77 + 100 or 177, consecutive interior angles are not supplementary. So, c is not parallel to a or b. Answer: a || b

6. Lesson 3-5 CYP 1 A. A B. B C. C D. D I only II only III only I, II, and III Determine which lines, if any are parallel. I. e || f II. e || g III. f || g

7. ALGEBRA Find x and m ZYN so that ||. Lesson 3-5 Example 2 Solve Problems with Parallel Lines ExploreFrom the figure, you know that m WXP = 11x – 25 and m ZYN = 7x + 35. You also know that WXP and ZYN are alternate exterior angles.

8. Lesson 3-5 Example 2 Solve Problems with Parallel Lines PlanFor line PQ to be parallel to MN, the alternate exterior angles must be congruent. So, m WXP = m ZYN. Substitute the given angle measures into this equation and solve for x. Once you know the value of x, use substitution to find m ZYN. Solve m WXP= m ZYN Alternate exterior angles 11x – 25= 7x + 35Substitution 4x – 25= 35Subtract 7x from each side. 4x=60Add 25 to each side. x= 15Divide each side by 4.

9. Lesson 3-5 Example 2 Solve Problems with Parallel Lines Now use the value of x to find m ZYN. Answer: x = 15, m ZYN = 140 m ZYN=7x + 35Original equation = 7(15) + 35x = 15 =140Simplify. ExamineVerify the angle measure by using the value of x to find m WXP. That is, 11x – 25 = 11(15) – 25 or 140. Since m WXP = m ZYN, m WXP m ZYN and ||.

10. Lesson 3-5 CYP 2 A. A B. B C. C D. D ALGEBRA Find x so that ||. x = 60 x = 9 x = 12

11. Lesson 3-5 Example 3 Prove Lines Parallel Prove: r || s Given: ℓ || m

12. Lesson 3-5 Example 3 Prove Lines Parallel 2.2. Consecutive Interior Angle Theorem 5. 5. Substitution 6.6. Definition of supplementary angles 7.7. If consecutive interior angles are supplementary, then lines are parallel. 1.1. Given Proof: StatementsReasons 4. 4. Definition of congruent angles 3.3. Definition of supplementary angles

13. Given x || y and, do you need to use the Corresponding Angles Postulate to prove a || b? A. A B. B C. C Lesson 3-5 CYP 3 yes no not enough information to determine

14. Lesson 3-5 Example 4 Determine whether p || q. Slope and Parallel Lines slope of p: slope of q: Answer: Since the slopes are equal, p || q.