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Warm ups

Warm ups. Make a conjecture about the next number in the sequence, 5, 20, 80, 320. Write the contrapositive of this statement. If you live in Boston, then you live in Massachusetts.

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Warm ups

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  1. Warm ups Make a conjecture about the next number in the sequence, 5, 20, 80, 320. Write the contrapositive of this statement. If you live in Boston, then you live in Massachusetts. 3. Find m<1 and m<2 if m<1 = 8x + 18 and m<2 = 16x – 6 and m<1 and m<2 are supplementary. 4. The measures of two complementary angles are x + 54 and 2x. What is the measure of the smaller angle?

  2. 3-1 Parallel Lines & Transversals Objective: Identify relationships between two lines or two planes. Name angle pairs formed by parallel lines and transversals.

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

  4. Concept

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

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

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

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

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

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

  11. Transversal Angle Pair Relationships

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

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

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

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

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

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

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

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

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

  21. Example 3 B. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting <2and <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. Identify Transversals and Classify Angle Pairs

  22. Example 3 C. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting <4and <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. Identify Transversals and Classify Angle Pairs

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

  24. Example 3b 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

  25. Example 3c 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

  26. Homework • Pg. 176 # 13 – 44, 50

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