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parallel lines & transversals lines

parallel lines & transversals lines

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parallel lines & transversals lines

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  1. Parallel Linesand Transversals

  2. Parallel Lines andTransversals What would you call two lines which do notintersect? Parallel B A solid arrowplaced on two lines of a diagram indicatethe lines areparallel. A D C Thesymbol || is used to indicate parallellines. AB || CD

  3. Parallel Lines andTransversals A slash through theparallelsymbol || indicates the lines are notparallel. B AB || CD A D C

  4. Parallel Lines andTransversals Transversal- A transversal is a line which intersects two or more lines inaplane. The intersected lines do not haveto beparallel. Lines j, k, andm areintersected by linet. Therefore, line t is atransversal of lines j, k,and m. j km t

  5. Parallel Lines andTransversals Identifying Angles- Exterior anglesare j k on the exteriorof the two lines cutby thetransversal. 1 3 5 6 7 8 t 2 4 The exterior anglesare: <1, <7, <2,<8

  6. Identifying Angles- Parallel Lines andTransversals Interiorangles j k are on the interiorof the two lines cutby thetransversal. 1 3 5 6 7 8 t 2 4 The interior anglesare: <3, <5, <4,<6

  7. Identifying Angles- Parallel Lines andTransversals Alternate interior angles are onthe interiorof the two lines and onopposite j k 1 3 5 6 7 8 t sides of the transversal. 2 4 Alternate interior anglesare: <3 & <6, <4 &<5

  8. Identifying Angles- Parallel Lines andTransversals Alternate j exterior angles are on the exteriorof the two lines andon oppositesides of the transversal. k 1 3 5 6 7 8 t 2 4 Alternate exterior anglesare: <1 & <8, <2 &<7

  9. Identifying Angles- Parallel Lines andTransversals Corresponding angles are onthe corresponding side of the two lines and on the sameside of the transversal. j k 1 3 5 6 7 8 t 2 4 Corresponding anglesare: <1&<5,<3&<7,<2&<6,<4&<8

  10. Parallel Lines andTransversals Identifying Angles – Check forUnderstanding Determine if the statement is trueorfalse. Iffalse, correct thestatement. 1. Line r is atransversal of lines p andq. 4 5 3 6 2 8 7 1 2. < 2 and < 10are alternate interiorangles. 9 16 10 11 12 15 14 13

  11. Parallel Lines andTransversals Identifying Angles – Check forUnderstanding Determine if the statement is trueorfalse. Iffalse, correct thestatement. 1. Line r is atransversal of lines p andq. True – Line rintersects both lines in aplane. 2. < 2 and < 10 are alternate interiorangles. False - The angles are corresponding angleson transversalp. 4 5 3 6 2 8 7 1 9 16 10 11 12 15 14 13

  12. Parallel Lines andTransversals Identifying Angles – Check forUnderstanding Determine if the statement is trueorfalse. Iffalse, correct thestatement. 1.<3and < 5 arealternate interiorangles. 4 5 3 6 2 8 7 1 4. < 1 and < 15are 9 10 alternate exteriorangles. 11 12 16 15 14 13

  13. Parallel Lines andTransversals Identifying Angles – Check forUnderstanding Determine if the statement is trueorfalse. Iffalse, correct thestatement. 3. <3 and < 5are alternate interiorangles. False – The anglesare vertical angles created by the intersection of q andr. 4 5 3 6 2 8 7 1 4. <1and < 15are 9 10 alternate exteriorangles. 11 12 16 15 14 13 True - The angles are alternate exterior angles on transversalp.

  14. Parallel Lines andTransversals Identifying Angles – Check forUnderstanding Determine if the statement is trueorfalse. Iffalse, correct thestatement. 5. < 6 and < 12are alternate interiorangles. 4 5 3 6 2 8 7 1 6. < 10 and < 11are 9 10 consecutive interiorangles. 11 12 16 15 14 13

  15. Parallel Lines andTransversals Identifying Angles – Check forUnderstanding Determine if the statement is trueorfalse. Iffalse, correct thestatement. 5. < 6 and < 12are alternate interiorangles. True – The angles are alternate interior angles on transversalq. 4 5 3 6 2 8 7 1 6. < 10 and < 11are 9 10 consecutive interiorangles. 11 12 16 15 14 13 True – The angles are consecutive interior angles on transversals.

  16. Parallel Lines andTransversals Identifying Angles – Check forUnderstanding Determine if the statement is trueorfalse. Iffalse, correct thestatement. 7. < 3 and < 4 arealternate exteriorangles. 4 5 3 6 2 8 7 1 8. <16 and < 14are 9 10 corresponding angles. 11 12 16 15 14 13

  17. Parallel Lines andTransversals Identifying Angles – Check forUnderstanding Determine if the statement is trueorfalse. Iffalse, correct thestatement. 7. < 3 and < 4 arealternate exteriorangles. False– The anglesare adjacent angles on transversalr. 4 5 3 6 2 8 7 1 8. <16 and < 14are 9 10 corresponding angles. 11 12 16 15 14 13 True – The anglesare corresponding angles on transversals.