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Understanding Corresponding Angles and Parallel Lines: Complete Lesson Overview

This comprehensive lesson focuses on the Corresponding Angles Postulate and its applications regarding parallel lines. Key concepts include identifying pairs of angles formed by transversals and parallel lines, using algebra to find angle measurements, and applying theorems like Alternate Interior Angles and Perpendicular Transversal Theorems. Gain insights through real-world examples and practice your understanding by solving problems. Engage with checks throughout the lesson to assess your grasp of these fundamental geometric principles.

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Understanding Corresponding Angles and Parallel Lines: Complete Lesson Overview

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Presentation Transcript

  1. Splash Screen

  2. Five-Minute Check (over Lesson 3–1) Then/Now Postulate 3.1: Corresponding Angles Postulate Example 1: Use Corresponding Angles Postulate Theorems: Parallel Lines and Angle Pairs Proof: Alternate Interior Angles Theorem Example 2: Real-World Example: Use Theorems about Parallel Lines Example 3: Find Values of Variables Theorem 3.4: Perpendicular Transversal Theorem Lesson Menu

  3. A B C D Choose the plane parallel to plane MNR. A.RST B.PON C.STQ D.POS 5-Minute Check 1

  4. A B C D Choose the segment skew to MP. ___ A.PM B.TS C.PO D.MQ ___ ___ ___ 5-Minute Check 2

  5. A B C D Classify the relationship between 1 and 5. A. corresponding angles B. verticle angles C. consecutive interior angles D. alternate exterior angles 5-Minute Check 3

  6. A B C D Classify the relationship between 3 and 8. A. alternate interior angles B. alternate exterior angles C. corresponding angles D. consecutive interior angles 5-Minute Check 4

  7. A B C D Classify the relationship between 4 and 6. A. alternate interior angles B. alternate exterior angles C. corresponding angles D. verticle angles 5-Minute Check 5

  8. A B C D Which of the following segmentsis not parallel to PT? A.OS B.TS C.NR D.MQ 5-Minute Check 6

  9. You named angle pairs formed by parallel lines and transversals. (Lesson 3–1) • Use theorems to determine the relationships between specific pairs of angles. • Use algebra to find angle measurements. Then/Now

  10. Concept

  11. Use Corresponding Angles Postulate A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used. 15  11 Corresponding Angles Postulate m15 =m11 Definition of congruent angles m15 =51 Substitution Answer: m15 = 51 Example 1

  12. Use Corresponding Angles Postulate B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used. 15  11 Corresponding Angles Postulate 15 16 Substitution 11 16 Supplement Theorem m11 = m16 Definition of Congruent Angles m16 = 51 Substitution Answer: m16 = 51 Example 1

  13. Mrs. Highman – Personal Tutor

  14. A B C D A. In the figure, a || b and m18 = 42. Find m22. A. 42 B. 84 C. 48 D. 138 Example 1a

  15. A B C D B. In the figure, a || b and m18 = 42. Find m25. A. 42 B. 84 C. 48 D. 138 Example 1b

  16. Concept

  17. Use Theorems about Parallel Lines FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3. 2  3 Alternate Interior Angles Postulate m2 =m3 Definition of congruent angles 125 =m3 Substitution Answer:m3 = 125 Example 2

  18. A B C D FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4. A. 25 B. 55 C. 70 D. 125 Example 2

  19. Find Values of Variables A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. 5  7 Corresponding Angles Postulate m5 =m7 Definition of congruent angles 2x – 10 =x + 15 Substitution x – 10= 15 Subtract x from each side. x = 25 Add 10 to each side. Answer:x = 25 Example 3

  20. Find Values of Variables B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y. 8  6 Corresponding Angles Postulate m8 = m6 Definition of congruent angles 4y = m6 Substitution Example 3

  21. Find Values of Variables m6 + m4 = 180 Supplement Theorem 4y + 4(y – 25) = 180 Substitution 4y + 4y – 100 = 180 Distributive Property 8y = 280 Add 100 to each side. y = 35 Divide each side by 8. Answer:y = 35 Example 3

  22. Mr. Hardesty – Personal Tutor

  23. A B C D A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x. A.x = 9 B.x = 12 C.x = 10 D.x = 14 Example 3

  24. A B C D B. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find y. A.y = 14 B.y = 20 C.y = 16 D.y = 24 Example 3

  25. Concept

  26. End of the Lesson

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