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Sect. 3.5 ** VOCAB STUDY GUIDE ** Name _______________________________________ I. Fill in each blank with the most specific vocabulary word (if there is no word, write NONE). Then identify which lines made the pair of angles. HINT/BIG IDEA: The transversal is the line that touches both ’s (i.e. the line the s have in common) It may help to highlight/darken the lines that are forming each angle. 1. 3 and 9 are ____________________________________________ (formed by transversal _____ and lines ______ & ____) 2. 3. 3 and 2 and 4. 5. 6. 7. 8. 9. 10 are __________________________________________ (formed by transversal _____ and lines ______ & ____) 10 are __________________________________________ (formed by transversal _____ and lines ______ & ____) 2 and 2 and 10. 11. 10 and 9 and 10 & 12. 10 and ’s (formed by transversal _____ and lines ______ & _____) 7 are ________________________________________________ ’s (formed by transversal _____ and lines ______ & _____) 7 are _______________________________________________ ’s (formed by transversal _____ and lines ______ & _____) 8 are _______________________________________________ ’s (formed by transversal _____ and lines ______ & _____) 5 are ______________________________________________ 12 are _____________________________________ ____ are consecutive interior 5 and 14. 8 are ________________________________________________ 8 and ’s (formed by transversal _____ and lines ______ & _____) 3 and ’s 6 are ________________________________________________ ’s 5 are _______________________________________________ ’s (formed by transversal _____ and lines ______ & _____) 2 and 13. 2 and ’s ____ are alternate interior ’s ; ’s (formed by transversal _____ and lines ______ & _____) 7& 8 are _______________________________________ ’s ’s (transversal ____ and lines ____ & ____). Are other answers possible? ______ ’s (transversal ____ and lines ____ & ____). Are other answers possible? ______ ____ are alternate exterior ’s (transversal ____ and lines ____ & ____). Are other answers possible? ______ 15. BIG IDEA (STUDY THIS!): Can we only call angles “alternate interior”, “alternate exterior”, “consecutive interior”, or “corresponding” angles IF the lines are parallel??? ______________ II. Use the diagram below to name each pair of angles, if possible (if not, write NONE”). 16. 9& 17. 18. 19. 20. 4& 9& 7& ’s (lines ___ & ___ & transv: ____) 9 are ___________________________ 16 are _________________________ 15 are __________________________ ’s (lines ___ & ___ & transv: ____) ’s (lines ___ & ___ & transv: ____) ’s (lines ___ & ___ & transv: ____) 4 & 7 are _________________________ ’s (lines ___ & ___ & transv: ___); so are 8 & 21. 22. 13 are _________________________ 1& 6& 13 are _________________________ 13 are _________________________ ’s (lines ___ & ___ & transv: ____) ’s (lines ___ & ___ & transv: ____) ____ (lines___&____; trans: ____) III. Parallel Lines (The Basics). Fill in the blanks with the name of a postulate or theorem, if possible. 23. If a || b, then 2 6 by ____________________________________________________________. 24. If a || b, then 1 7 by ____________________________________________________________. 25. If a || b, then 3 5 by ____________________________________________________________. 26. If a || b, then 3 6 by ____________________________________________________________. 27. If a || b, then 3 & 6 are supplementary by _________________________________________. 28. If a || b, then 1 6 by _______________________________________________________________. 29. If a || b, then 2 8 by _______________________________________________________________. 30. If a || c, why can’t we use the Corresponding Angles Post. to say that 3 7? 31. BIG IDEA: We can only use the Corresponding s Post., the Alternate Interior s Thm, the Alternate Exterior s Thm, & the Consecutive Interior s Thm IF we know the relevant lines are _______________ IV. Answer the questions using the diagram to the right 32. True or False: 11 15 because they are corresponding angles. 33. True or False: 3 6 by Alternate Exterior Angles Theorem. 34. True or False: 7 15 by Corresponding Angles Postulate. 35. True or False: 12 & 15 are supplementary by Consecutive Interior Angles Theorem. 36. BIG IDEA: #32-#35 all used relevant/accurate vocab words. However, the use of signs (& the word “supplementary” in #35) made all of these statements FALSE…. because we did not know whether the lines were _____________________________. (Remember: All of the thms/post. about these types of angles being congruent (or “supplementary” for consec. int. angles) start with the same hypothesis: “If 2 parallel lines are cut….”) V. Use the same diagram from above (with lines n, p, r, & s) BUT this time, you are being GIVEN that n || p. 37. True or False: 11 15 by the Corresp. s Post. 38. True or False: 3 6 by the Alt. Ext. s Thm. 39. True or False: 12 & 15 are suppl. by Cons. Int. s Thm. 40. True or False: 2 5 by Consec. Int. s Thm. VI. Given: n || p in the diagram above, fill in each blank with the name of a thm/post/def, if possible: 41. 7 14 by ________________________________________ 43. 7 15 by ________________________________________ 42. 44. 6 15 by ________________________________________ 8 & 14 are suppl. by ____________________________ 45. Under each question from #41 – 44, list the transversal & 2 other lines that formed each pair of angles. 46. After completing #45, you should realize that #41 - #44 were all not possible. The statements involved angles that were NOT formed by the given parallel lines (n & p). Thus, #41 - #44 were all false/not possible! VII. Fill in the blanks using the diagram below. To make it easier for us to check answers, name each line using the points that are on the far “ends” of the line. Ex: Name the slanted line as GI instead of GM or MF . etc. 47. GMO and Hint: MSI are not corresponding angles. Why not? GMO is formed by lines _________ and ________. MSI is formed by lines _________ and _________. Is there a line in common, i.e. a transversal that helps form both 48. MSI and s? TMF are not alternate exterior angles. Why not? Hint: What would the transversal be? Remember, the transversal is the line that both 49a. s have in common. FMS and MSI are ______________________________________ s (formed by transversal: _______ & lines: ________& ________) b. TMS and MSI are ______________________________________ s (formed by transversal: _______ & lines: ________& ________) c. If OY || IU , only 1 of the above pairs of Alternate Interior s is congruent. Which pair is it? Why? 50a. MTF and TFS are ______________________________________ b. MTF and TFM are ______________________________________ s (formed by transversal: _______ & lines: ________& ________) s (formed by transversal: _______ & lines: ________& ________) c. If OY || IU , only 1 of the above pairs of Consecutive Interior s is supplementary. Which pair is it? Why? 51a. GMO and MFS are _____________________________________ s (formed by transversal: _______ & lines: ________& ________) b. If EN || RH , can you conclude anything about GMO & MFS? If so, what? What thm/post did you use? c. If OY || IU , can you conclude anything about GMO & MFS? If so, what? What thm/post did you use? 52. If EN || RH , can we say that EMO FSN? If so, what thm/post did you use? If not, explain why not. 53a. If EN || RH then, by Alternate Exterior Angles Thm, ISN _____ and OMS _______. (For the first pair of angles, line ______ is the transversal; for the second pair, ______ is the transversal) b. If EN || RH , why can’t we say that 54. Are RTY SFHby the Alternate Exterior Angles Thm? EMO & SFT alternate interior, alternate exterior, consecutive interior, or corresponding s? Explain. ANSWER KEY: 1. consecutive interior (transversal b, lines c & a) 2. alternate interior (transversal b, lines c & a) 3. corresponding (transversal b, lines c & a) 4. consecutive interior (transversal c, lines b & a) 5. corresponding (transversal c, lines b & a) 6. NONE (transv: c, lines b & a)….these are on opp. sides of the transversal c, but 2 is in the interior & 8’s in the exterior. 7. alternate interior (transversal c, lines b & a) 8. consecutive interior (transversal a, lines b & c) 9. alternate interior (transversal a, lines b & c) 10. NONE (transv. a, lines b & c)….both are exterior angles, & on same side of transversal. 11. vertical; linear pair/adjacent/supplementary (REVIEW!) 12. 11 (transversal a, lines c & b). No other angles besides 11 would work here. [If you try to use 4, then 8 would be an EXTERIOR angle, so it doesn’t work. Can’t say 7 either because 8 & 7 are adjacent] 13. 10 (transversal b, lines c & a). No other angles besides 10 would work here. [If you try to use 5, then 3 would be an EXTERIOR angle, so it doesn’t work. Can’t say 4 either because 3 & 4 are adjacent] 14. 12 (transversal a, lines c & b). No other angles besides 12 would work here. [If you try to use 3, then 5 would be an INTERIOR angle, so it doesn’t work. Can’t say 6 either because 5 and 6 are adjacent] 15. No. BIG IDEA: We can use the vocab words “alternate interior”, “alternate exterior”, “consecutive interior”, & “corresponding” to describe angles for both parallel & intersecting lines. This is possible because the definitions of these vocabulary words don’t specify/mention that the lines have to be parallel! II. 16. 17. 18. 19. 20. 21. 22. corresponding (lines n & p, transversal: s) alternate interior (lines r & s, transversal: n) alternate exterior (lines n & p, transversal: s) corresponding (lines r & s, transversal: p) consecutive interior (lines n & p, transversal: r); so are 8 and 14 (lines r & s, transversal: p) NONE (there is no transversal in common for these two angles) NONE ( 6 is an exterior angle and 13 is an interior angle. They are on diff. sides of transversal. No vocab!) III. 23. 24. 25. 26. 27. 28. 29. 30. Corresponding Angles Postulate Alternate Exterior Angles Theorem Alternate Interior Angles Theorem NONE. These are Consecutive Interior Angles. If the lines are ||, these must be supplementary (not necessarily ) Consecutive Interior Angles Theorem NONE. ( 1 is an exterior angle & 6 is an interior angle. They are on diff. sides of transv. No vocab!) Alternate Exterior Angles Theorem 3 & 7 are formed by transversal t & lines a & b. This statement said a || c, not a || b. We can only use the Corresponding s Postulate if the 2 lines that form the corresponding s are parallel. We don’t know if a || b. 31. Parallel. BIG IDEA: We can only use the Corresponding s Post., the Alternate Interior s Thm, the Alternative Exterior s Thm, & the Consec. Interior s Thm IF we know the relevant lines are PARALLEL IV. 32. 33. 34. 35. 36. False. We can call these corresponding ’s but we can’t say they are because we don’t know whether n || p. False. We can call these alternate exterior ’s but we can’t say they are because we don’t know whether n || p False. We can call these corresponding ’s but we can’t say they are because we don’t know whether r || s. False. We can call these consecutive int. ’s but we can’t saythey are suppl. because we don’t know whether n || p Parallel V. 37. True 38. True 39. True 40. False. These are consec. int. angles that are on our || lines n & p but if the lines are ||, consec. int. angles are always suppl. (not ) VI. if r || s) 41. No post/thm/def exists (these two alt. int ’s are formed by transversal p and lines r & s….but we don’t know 42. No post/thm/def exists (these two alt. ext. ’s are formed by transversal p and lines r & s….but we don’t know if r || s) 43. No post/thm/def exists (these two corres. ’s are formed by transversal p and lines r & s….but we don’t know if r || s) 44. No post/thm/def exists (these two consec int ’s are formed by transv. p & lines r & s….but we don’t know if r || s) 45. See above parentheses 46. [No answer needed. This “problem” was just a statement about the above answers] VII. 47. GMO: formed by GI & OY ; MSI : formed by EN & IU . No transversal is in common/helps form both of these angles. 48. MSI : formed by EN & IU ; TMF: formed by OY & GI . No transversal is in common/helps form both of these angles. 49a. alternate interior angles (transversal b. alternate interior angles (transversal c. MTF and EN and lines GI & IU ) EN and lines OY & IU ) are formed TFS because they by thetwo lines we know are parallel ( OY & IU ) 50a. consecutive interior angles (transversal RH and lines OY & IU ) b. consecutive interior angles (transversal RH and lines OY & GI ) c. TMS and formed by the two lines we know are parallel ( OY & IU ) MSF are supplementary because they are 51a. corresponding angles (transversal GI and lines OY & IU ) b. We can’t say anything since the || lines here ( EN and RH ) are NOT the same lines that make these s ( OY & IU ). c. GMO MFS by the Corresponding Angles Postulate 52. No. These angles are alternate exterior ’s, but they are NOT formed by the TWO || lines EN and RH . Instead, these angles are formed by OY & IU (with transversal: EN )….so we would need to know that OY || IU to say these are 53a. First blank: RFU (or TFU….they’re the same angle) Transversal: IU Second blank: RTY Transversal: OY b. These angles are not formed by the parallel lines EN and RH . These angles formed by lines OY & IU (with transversal: RH )….and we don’t know if OY || IU 54. No vocab words apply here because these two angles have no transversal in common.
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