2. Course: Applied Geometry Aim: 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. 10x - 18 5x - 12 7x - 40 8x + 10 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.

3. Course: Applied Geometry Aim: Parallel Lines 10x - 18 5x - 12 7x - 40 8x + 10 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 + 5x - 12 = 180 5x - 12 + 8x + 10 = 180 8x + 10 + 7x - 40 = 180 7x - 40 + 10x - 18 = 180 x = 14 Do Now:

4. Course: Applied Geometry Aim: Parallel Lines A line that intersects more than one line is called a transversal. l p m is a transversal m

5. Course: Applied Geometry Aim: Parallel Lines Exterior zone Zones formed by l m Interior zone Exterior zone p

6. Course: Applied Geometry Aim: Parallel Lines Alternate Sides formed by l p m Exterior zone Interior zone

7. Course: Applied Geometry Aim: Parallel Lines The Importance of Parallel

8. Course: Applied Geometry Aim: Parallel Lines 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” p DC l A B AB | | CD or l | | p

9. Course: Applied Geometry Aim: Parallel Lines Angles formed by l p m 4 1 5 8 2 3 6 7  2 and  3 are congruent vertical angles  6 and  7 are congruent vertical angles l | | p If l | | p then  2   3   6   7

10. Course: Applied Geometry Aim: Parallel Lines Angles formed by l p m 2 43 1 56 7 8  1 and  4 are congruent vertical angles  5 and  8 are congruent vertical angles Since l | | p then  1   4   5   8 l | | p

11. Course: Applied Geometry Aim: Parallel Lines l p m 1 8 2 7  1 and  8 are alternate exterior angles  2 and  7 are alternate exterior angles If l | | p then  1   8 If l | | p then  2   7 A Alternate Exterior Angles Alternate ExteriorAngles If two parallel lines are cut by a transversal, then the Alternate Exterior Angles formed are congruent. 43 56

12. Course: Applied Geometry Aim: Parallel Lines l p m 21 7 8 4 5 3 6  3 and  6 are alternate interior angles  4 and  5 are alternate interior angles If l | | p then  3   6 If l | | p then  4   5 A Alternate InteriorAngles Alternate Interior Angles Alternate InteriorAngles If two parallel lines are cut by a transversal, then the Alternate Interior Angles formed are congruent.

13. Course: Applied Geometry Aim: Parallel Lines l p m 21 7 8 3 5 4 6  3 and  5 are interior angles  3 and  6 are interior angles If l | | p then  3 &  5 are supplementary InteriorAngles on Same Side Interior Angles on Same Side InteriorAngles If two parallel lines are cut by a transversal, then the Interior Angles on the same side of the transversal are supplementary.

14. Course: Applied Geometry Aim: Parallel Lines l p m 2 43 1 56 7 8 Corresponding Angles A Corresponding Angles If two parallel lines are cut by a transversal, then the Corresponding Angles formed are congruent.  3 and  7  2 and  6  1 and  5  4 and  6  3   7  2   6  1   5  4   6 If l | | p then

15. Course: Applied Geometry Aim: Parallel Lines l p m l is parallel to m wx yz q p r s Name the exterior anglesName the interior anglesName the corresponding anglesName the alternate interior anglesName the alternate exterior angles

16. Course: Applied Geometry Aim: Parallel Lines l p m Find the measure of each angle if  1 = 137 0. 1 3 4 5 6 7 8 43 0 137 0 43 0 137 0 43 0 137 0 2 43 0 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.

17. Course: Applied Geometry Aim: Parallel Lines AB | | CD Find the measure of each angle if  AHF = 8x - 20 and  CGH = 4x + 44. 108 0 E G C D H B F  AHF and  CGH are Corresponding Angles and therefore are congruent 8x - 20 = 4x + 44 4x - 20 = 44 4x = 64 x = 16 8(16) - 20 = 108 0 108 0 A 180 0 - 108 0 = 72 0 72 0

18. Course: Applied Geometry Aim: Parallel Lines The measure of  b is twice the measure of  a. What is the measure of each angle. C D B F A b a AB | | CD

19. Course: Applied Geometry Aim: Parallel Lines The measure of  a is five times the measure of  b. What is the measure of  y. C D B F A b a AB | | CD y

20. Course: Applied Geometry Aim: Parallel Lines Give two ways to find the measure of  y. C D B F A zx AB | | CD 150 o y

21. Course: Applied Geometry Aim: Parallel Lines Find the measure of all angles. C D B G A q p AB | | CD | | EF 75 o E F o s r v u x w z y

22. Course: Applied Geometry Aim: Parallel Lines Skew Lines Lines in space that never meet and are not in the same plane are skew lines. A B C D E F