1 / 21

Aim: What are Transversals and Angle Pairs? Parallel Lines?

Aim: What are Transversals and Angle Pairs? Parallel Lines?. Do Now: Below are 2 intersecting straight lines. Describe 2 different methods of finding the value of x.

Download Presentation

Aim: What are Transversals and Angle Pairs? Parallel Lines?

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. Aim: What are Transversals and Angle Pairs? Parallel Lines? Do Now: Below are 2 intersecting straight lines. Describe 2 different methods of finding the value of x. 1. Intersecting lines form vertical angles that are opposite each other and congruent. Therefore you can find the value of x by putting 10x - 18 = 8x + 10 or 7x - 40 = 5x - 12 and solving for x. 10x - 18 7x - 40 5x - 12 8x + 10

  2. Do Now: 2. There are 4 linear pair in this diagram: angles that are adjacent and supplementary. Therefore you can find the value of x by solving any of four equations: 10x - 18 7x - 40 5x - 12 8x + 10 10x - 18 + 5x - 12 = 180 5x - 12 + 8x + 10 = 180 8x + 10 + 7x - 40 = 180 7x - 40 + 10x - 18 = 180 x = 14

  3. m m is a transversal l p Transversals A line that intersects more than one line is called a transversal.

  4. Exterior zone Interior zone Exterior zone Zones formed by Transversals m l p

  5. Alternate Sides formed by Transversals m Exterior zone l Interior zone p Exterior zone

  6. The Importance of Parallel

  7. Parallel Lines Parallel Lines A B l AB | | CD or l| |p p C D Two or more lines are parallel if and only if the lines lie in the same plane but do not intersect. | | means “is parallel to”

  8. Angles formed by Transversals l | | p m 1 2 l 3 4 5 6 7 8 p 2 and 3 are congruent vertical angles 6 and 7 are congruent vertical angles If l | | p then 2  3  6  7

  9. Angles formedby Transversals m l | | p 1 2 l 3 4 5 6 7 8 p 1 and 4 are congruent vertical angles 5 and 8 are congruent vertical angles Since l | | p then 1  4  5  8

  10. 1 2 7 8 Alternate Exterior Angles m l 3 4 5 6 p 1 and 8 are alternate exterior angles If l | | p then 1  8 2 and 7 are alternate exterior angles If l | | p then 2  7 A If two parallel lines are cut by a transversal, then the Alternate ExteriorAngles formed are congruent.

  11. 3 4 5 6 Alternate InteriorAngles m 1 2 l 7 8 p 3 and 6 are alternate interior angles If l | | p then 3  6 4 and 5 are alternate interior angles If l | | p then 4  5 A If two parallel lines are cut by a transversal, then the Alternate InteriorAngles formed are congruent.

  12. 3 4 5 6 InteriorAngles on Same Side m 1 2 l 7 8 p 3 and 5 are interior angles If l | | p then 3 & 5 are supplementary 3 and 6 are interior angles If l | | p then 3 & 5 are supplementary If two parallel lines are cut by a transversal, then the InteriorAngles on the same side of the transversal are supplementary.

  13. 1 and 5 2 and 6 If l | | p then 3 and 7 4 and 6 Corresponding Angles m 1 2 l 3 4 5 6 7 8 p Corresponding Angles 1  5 2  6 3  7 4  6 A If two parallel lines are cut by a transversal, then the Corresponding Angles formed are congruent.

  14. l is parallel to m Name the alternate exterior angles Name the corresponding angles Name the interior angles Name the exterior angles Name the alternate interior angles m l w x z y p q s r p

  15. Find the measure of each angle if 1 = 1370. m 1370 430 l 1 2 4 3 430 1370 1370 430 6 5 7 8 p 430 1370 Note: 1 and 2 are a linear pair. How many other linear pairs are there in this diagram? 7 other linear pairs - 2 & 4; 4 & 3; 3 & 1; 5 & 6; 6 & 8; 8 & 7; and 7 & 5.

  16. AB | | CD Find the measure of each angle if AHF = 8x - 20 and CGH = 4x + 44. F 720 1080 A B 720 H 1080 1080 720 G D 720 C 1080 AHF and CGH are Corresponding Angles and therefore are congruent E 8(16) - 20 = 1080 8x - 20 = 4x + 44 1800 - 1080 = 720 4x - 20 = 44 4x = 64 x = 16

  17. The measure of b is twice the measure of a. What is the measure of each angle. AB | | CD A B a b D C F

  18. The measure of a is five times the measure of b. What is the measure of y. AB | | CD y A B a b D C F

  19. Give two ways to find the measure of y. AB | | CD 150o x z A B y D C F

  20. Find the measure of all angles. AB | | CD | | EF o 75o A p q B r s C u v D w x E y z F G

  21. E D B C A F Skew Lines Lines in space that never meet and are not in the same plane are skew lines.

More Related