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3-1 – Definitions

3-1 – Definitions. Definitions. Parallel Lines ( ) – Skew Lines – Parallel Planes – Line Parallel to a Plane – Transversal – . Always, Sometimes, or Never?. Two lines in the same plane are _____________ parallel. Two lines in the same plane are _____________ skew.

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3-1 – Definitions

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  1. 3-1 – Definitions

  2. Definitions • Parallel Lines () – • Skew Lines – • Parallel Planes – • Line Parallel to a Plane – • Transversal –

  3. Always, Sometimes, or Never? • Two lines in the same plane are _____________ parallel. • Two lines in the same plane are _____________ skew. • Two noncoplanar lines _____________ intersect. • Two planes _____________ intersect. • A line and a plane _____________ have exactly one point of intersection. • If two planes do not intersect, then they are _____________ parallel.

  4. Name the two lines and the transversal that form each pair of angles k l • A.) and B.) and • A.) and B.) and 2 n 1 3 a b 4 5 c d 6

  5. Name the two lines and the transversal that form each pair of angles B C D • A.) and B.) and • A.) and B.) and 4 2 1 3 A E G H 7 8 5 6 I F K J

  6. x y Angles t 1 2 3 4 6 5 8 7 • Exterior Angles – • Interior Angles – • Alternate Interior Angles – • Same-Side Interior Angles – • Corresponding Angles –

  7. Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles. • and • and • and • and • and • and a b c 3 4 2 1 7 8 6 5 9 10 11 12 d 13 14 15 16

  8. Classify each pair of angles as alternate interior angles, same-side interior angles, or corresponding angles. • and • and • and • and • and • and • and • and U V W X S Y T Z Q P R

  9. 3-2 – Properties of Parallel Lines

  10. Properties of Parallel Lines • If two _________________ lines are cut by a _________________, then corresponding angles are _________________. • If two _________________ lines are cut by a _________________, then alternate interior angles are _________________. • If two _________________ lines are cut by a _________________, then same-side interior angles are _________________. • If a _________________ is perpendicular to one of two _________________ lines, then it is _________________ to the other one also.

  11. State the postulate or theorem that justifies each statement. a b 1 3 4 j 6 5 2 7 8 k - (Arrowheads) Used to represent parallel lines

  12. State the postulate or theorem that justifies each statement. a b • is supplementary to 1 3 4 j 6 5 2 7 8 k

  13. Understanding Properties of Parallel Lines • Name seven angles that must be congruent to . • Name the eight angles that must be supplementary to . • If , what are the measures of the other numbered angles? 1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16

  14. Complete • If , then and . • If , then and . • If , then and . • If , then and . 12 9 4 1 11 10 3 2 16 13 8 5 15 14 7 6

  15. Complete • If , find . • If , find . 12 9 4 1 11 10 3 2 16 13 8 5 15 14 7 6

  16. Complete the following proof by supplying the missing statements and reasons. P Given: ; Prove: 1 3 T S 2 Q R

  17. Complete the following proof by supplying the missing statements and reasons. t k 1 Given: ; Prove: l 2

  18. Reminder! • If two parallel lines are cut by a transversal, then Corresponding angles are congruent, Alternate Interior angles are congruent, and Same-Side Interior angles are supplementary • If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also.

  19. Find the values of x and y. 1. 2. 3y˚ 6y˚ 5x˚ 5y˚ 8x˚ 4x˚

  20. Find the values of x and y. 3. 4. 140y˚ y˚ (2x+10)˚ x˚ 40˚ y˚ 70˚

  21. Find the values of x and y. 5. 6. 65˚ x˚ y˚ 55˚ x˚ 50˚ y˚ 40˚

  22. Find the values of x, y, and z. 7. 8. y˚ 30˚ x˚ 42˚ 6z˚ (3z+8)˚ (4y+14)˚ 70˚ x˚

  23. Find the values of x, y, and z. 9. 10. 5z˚ 3x˚ 60˚ (2y+10)˚ 2z˚ 5y˚ 40˚ x˚

  24. Complete the following proof by supplying the missing statements and reasons. B A Given: Prove: 1 3 2 5 4 D C

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