1 / 26

LESSON 3–2

LESSON 3–2. Angles and Parallel Lines. Five-Minute Check (over Lesson 3–1) TEKS 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

ldyer
Download Presentation

LESSON 3–2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. LESSON 3–2 Angles and Parallel Lines

  2. Five-Minute Check (over Lesson 3–1) TEKS 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. Choose the plane parallel to plane MNR. A.RST B.PON C.STQ D.POS 5-Minute Check 1

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

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

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

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

  9. Targeted TEKS G.6(A) Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems. Mathematical Processes G.1(A), G.1(G) TEKS

  10. You named angle pairs formed by parallel lines and transversals. • Use theorems to determine the relationships between specific pairs of angles. • Use algebra to find angle measurements. Then/Now

  11. Concept

  12. 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

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

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

  15. 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. Concept

  18. 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 Theorem m2 =m3 Definition of congruent angles 125 =m3 Substitution Answer:m3 = 125 Example 2

  19. 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

  20. Find Values of Variables A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. Explain your reasoning 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

  21. 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

  22. 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

  23. 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. 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. LESSON 3–2 Angles and Parallel Lines

More Related