1 / 24

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.

hila
Download Presentation

3-1 – Definitions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related