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Parallel and Skew Relationships in Geometry

This lesson covers parallel and skew relationships in geometry, including identifying parallel and skew lines, classifying angle pairs, and identifying transversals. Examples and vocabulary concepts are provided.

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Parallel and Skew Relationships in Geometry

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  1. Splash Screen

  2. Five-Minute Check (over Chapter 2) Then/Now New Vocabulary Key Concepts: Parallel and Skew Example 1: Real-World Example: Identify Parallel and Skew Relationships Key Concepts: Transversal Angle Pair Relationships Example 2: Classify Angle Pair Relationships Example 3: Identify Transversals and Classify Angle Pairs Lesson Menu

  3. A B C D Make a conjecture about the next number in the sequence, 5, 20, 80, 320. A. 380 B. 395 C. 1280 D. 1580 5-Minute Check 1

  4. A B C D Write the contrapositive of this statement. If you live in Boston, then you live in Massachusetts. A. If you do not live in Massachusetts, then you do not live in Boston. B. If you live in Massachusetts, then you do not live in Boston. C. If you do not live in Massachusetts, then you live in Boston. D. You might live in Massachusetts or Boston. 5-Minute Check 2

  5. A B Use the Law of Detachment or the Law of Syllogism to determine whether a valid conclusion can be reached from the following set of statements. If two angles form a linear pair and are congruent, they are both right angles. A and B are both right angles. A. Yes, A and B are a linear pair. B. no conclusion 5-Minute Check 3

  6. A B C D Name the property that justifies the statement.If m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75. A. Substitution Property B. Reflexive Property C. Addition Property D. Symmetric Property 5-Minute Check 4

  7. A B C D Find m1 and m2 if m1 = 8x + 18 and m2 = 16x – 6 and m1 and m2 are supplementary. A.m1 = 106, m2 = 74 B.m1 = 74, m2 = 106 C.m1 = 56, m2 = 124 D.m1 = 14, m2 = 166 5-Minute Check 5

  8. A B C D The measures of two complementary angles are x + 54 and 2x. What is the measure of the smaller angle? A. 24 B. 42 C. 68 D. 84 5-Minute Check 6

  9. You used angle and line segment relationships to prove theorems. (Lesson 2–8) • Identify relationships between two lines or two planes. • Name angle pairs formed by parallel lines and transversals. Then/Now

  10. parallel lines • skew lines • parallel planes • transversal • interior angles • exterior angles • consecutive interior angles • alternate interior angles • alternate exterior angles • corresponding angles Vocabulary

  11. Concept

  12. A. Name all segments parallel to BC. Answer:AD, EH, FG Identify Parallel and Skew Relationships Example 1

  13. B. Name a segment skew to EH. Answer:AB, CD, BG, or CF Identify Parallel and Skew Relationships Example 1

  14. Identify Parallel and Skew Relationships C. Name a plane parallel to plane ABG. Answer: plane CDE Example 1

  15. A B C D A. Name a plane that is parallel to plane RST. A. plane WTZ B. plane SYZ C. plane WXY D. plane QRX Example 1a

  16. A B C D B. Name a segment that intersects YZ. A.XY B.WX C.QW D.RS Example 1b

  17. A B C D C. Name a segment that is parallel to RX. A.ZW B.TZ C.QR D.ST Example 1c

  18. Concept

  19. Classify Angle Pair Relationships A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: corresponding Example 2

  20. Classify Angle Pair Relationships B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate exterior Example 2

  21. Classify Angle Pair Relationships C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: consecutive interior Example 2

  22. Classify Angle Pair Relationships D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles. Answer: alternate interior Example 2

  23. A B C D A. Classify the relationship between 4 and 5. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior Example 2a

  24. A B C D B. Classify the relationship between 7 and 9. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior Example 2b

  25. A B C D C. Classify the relationship between 4 and 7. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior Example 2c

  26. A B C D D. Classify the relationship between 2 and 11. A. alternate interior B. alternate exterior C. corresponding D. consecutive interior Example 2d

  27. Identify Transversals and Classify Angle Pairs A. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 1 and 2. Then classify the relationship between the pair of angles. Answer: The transversal connecting 1 and 2 is line v. These are corresponding angles. Example 3

  28. Identify Transversals and Classify Angle Pairs B. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 2 and 3. Then classify the relationship between the pair of angles. Answer: The transversal connecting 2 and 3 is line v. These are alternate interior angles. Example 3

  29. Identify Transversals and Classify Angle Pairs C. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 4 and 5. Then classify the relationship between the pair of angles. Answer: The transversal connecting 4 and 5 is line y. These are consecutive interior angles. Example 3

  30. A B C D A. HIKING A group of nature trails is shown. Identify the sets of lines to which line a is a transversal. A. lines c, f B. lines c, d, e C. lines c, d, f D. lines c, d, e, f Example 3a

  31. A B C D B. HIKING A group of nature trails is shown. Identify the sets of lines to which line b is a transversal. A. no lines B. lines c, f C. lines c, d, e, f D. lines a, c, d, e, f Example 3b

  32. A B C D C. HIKING A group of nature trails is shown. Identify the sets of lines to which line c is a transversal. A. no lines B. lines a, b, d, e, f C. lines a, d, f D. lines a, b, e Example 3c

  33. End of the Lesson

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