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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.

jamal-stevens
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Aim: What are Transversals and Angle Pairs? Parallel Lines?

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  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.

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