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Splash Screen. Five-Minute Check (over Lesson 3–4) CCSS Then/Now Postulate 3.4: Converse of Corresponding Angles Postulate Postulate 3.5: Parallel Postulate Theorems: Proving Lines Parallel Example 1: Identify Parallel Lines Example 2: Standardized Test Example: Use Angle Relationships

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  1. Splash Screen

  2. Five-Minute Check (over Lesson 3–4) CCSS Then/Now Postulate 3.4: Converse of Corresponding Angles Postulate Postulate 3.5: Parallel Postulate Theorems: Proving Lines Parallel Example 1: Identify Parallel Lines Example 2: Standardized Test Example: Use Angle Relationships Example 3: Real-World Example: Prove Lines Parallel Lesson Menu

  3. containing the point (5, –2) in point-slope form? A. B. C. D. 5-Minute Check 1

  4. What is the equation of the line with slope 3 containing the point (–2, 7) in point-slope form? A.y = 3x + 7 B.y = 3x – 2 C.y – 7 = 3x + 2 D.y – 7 = 3(x + 2) 5-Minute Check 2

  5. What equation represents a line with slope –3 containing the point (0, 2.5) in slope-intercept form? A.y = –3x + 2.5 B.y = –3x C.y – 2.5 = –3x D.y = –3(x + 2.5) 5-Minute Check 3

  6. containing the point (4, –6) in slope-intercept form? A. B. C. D. 5-Minute Check 4

  7. What equation represents a line containing points (1, 5) and (3, 11)? A.y = 3x + 2 B.y = 3x – 2 C.y – 6 = 3(x – 2) D.y – 6 = 3x + 2 5-Minute Check 5

  8. A. B. C. D. 5-Minute Check 6

  9. Content Standards G.CO.9 Prove theorems about lines and angles. G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. CCSS

  10. You found slopes of lines and used them to identify parallel and perpendicular lines. • Recognize angle pairs that occur with parallel lines. • Prove that two lines are parallel. Then/Now

  11. Concept

  12. Concept

  13. Concept

  14. A. Given 1  3, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. Identify Parallel Lines 1 and 3 are corresponding angles of lines a and b. Answer:Since 1  3, a║b by the Converse of the Corresponding Angles Postulate. Example 1

  15. B. Given m1 = 103 and m4 = 100, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer. Identify Parallel Lines 1 and 4 are alternate interior angles of lines a and c. Answer:Since 1 is not congruent to 4, line a is not parallel to line c by the Converse of the Alternate Interior Angles Theorem. Example 1

  16. A. Given 1  5, is it possible to prove that any of the lines shown are parallel? A. Yes; ℓ║ n B. Yes; m ║ n C. Yes; ℓ║ m D. It is not possible to prove any of the lines parallel. Example 1

  17. B. Given m4 = 105 and m5 = 70, is it possible to prove that any of the lines shown are parallel? A. Yes; ℓ║ n B. Yes; m║ n C. Yes; ℓ║ m D. It is not possible to prove any of the lines parallel. Example 1

  18. Find mZYN so that || . Show your work. Use Angle Relationships Read the Test Item From the figure, you know that mWXP = 11x – 25 and mZYN = 7x + 35. You are asked to find mZYN. Example 2

  19. m WXP = m ZYN Alternate exterior angles Use Angle Relationships Solve the Test ItemWXP and ZYN are alternate exterior angles. For line PQ to be parallel to line MN, the alternate exterior angles must be congruent. Som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 findmZYN. 11x – 25 = 7x + 35 Substitution 4x – 25 = 35 Subtract 7x from each side. 4x = 60 Add 25 to each side. x = 15 Divide each side by 4. Example 2

  20. Since mWXP = mZYN,WXP ZYNand || . Use Angle Relationships Now use the value of x to findmZYN. mZYN = 7x + 35 Original equation = 7(15) + 35 x= 15 = 140 Simplify. Answer:mZYN = 140 Check Verify the angle measure by using the value of x to find mWXP. mWXP = 11x – 25 = 11(15) – 25 = 140 Example 2

  21. ALGEBRA Find x so that || . A.x = 60 B.x = 9 C.x = 12 D.x = 12 Example 2

  22. End of the Lesson

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