1. 3.3 ll Lines & Transversals p. 143

2. Definitions Parallel lines (ll) – lines that are coplanar & do not intersect. (Have the some slope. ) l ll m Skew lines – lines that are not coplanar & do not intersect. Parallel planes – 2 planes that do not intersect. Example: the floor & the ceiling l m

3. H G D C A B E F 1. Line AB & Line DC are _______. 2. Line AB & Line EF are _______. 3. Line BC & Line AH are _______. 4. Plane ABC & plane HGF are _______. 1.Parallel 2.Parallel 3.Skew 4.Parallel

4. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Transversal A line that intersects 2 or more coplanar lines at different points. lmlm t

5. 1 2 3 4 5 6 7 8 Interior <s - <3, <4, <5, <6 (inside l & m ) Exterior <s - <1, <2, <7, <8 (outside l & m ) Alternate Interior <s - <3 & <6, <4 & <5 (alternate –opposite sides of the transversal) Alternate Exterior <s - <1 & <8, <2 & <7 Consecutive Interior <s - <3 & <5, <4 & <6 (consecutive – same side of transversal) Corresponding <s - <1 & <5, <2 & <6, <3 & <7, <4 & <8 (same location)

6. Post. 15 – Corresponding  s Post. If 2  lines are cut by a transversal, then the pairs of corresponding  s are . i.e. If l  m, then  1  2. l m 1 2

7. Thm 3.4 – Alt. Int.  s Thm. If 2  lines are cut by a transversal, then the pairs of alternate interior  s are . i.e. If l  m, then  1  2. lmlm 1 2

8. Proof of Alt. Int.  s Thm. Statements 1.l  m 2.  3   2 3.  1   3 4.  1   2 Reasons 1.Given 2.Corresponding  s post. 3.Vert.  s Thm 4.   is transitive lmlm 1 2 3

9. Thm 3.5 – Consecutive Int.  s thm If 2  lines are cut by a transversal, then the pairs of consecutive int.  s are supplementary. i.e. If l  m, then  1 &  2 are supp. lmlm 1 2

10. Thm 3.6 – Alt. Ext.  s Thm. If 2  lines are cut by a transversal, then the pairs of alternate exterior  s are . i.e. If l  m, then  1  2. l m 1 2

11. Thm 3.7 -  Transversal Thm. If a transversal is  to one of 2  lines, then it is  to the other. i.e. If l  m, & t  l, then t  m. **  1 & 2 added for proof purposes. 1 2 lmlm t

12. Proof of  transversal thm Statements 1.l  m, t  l 2.  1  2 3.m  1=m  2 4.  1 is a rt.  5.m  1=90 o 6.90 o =m  2 7.  2 is a rt.  8.t  m Reasons 1.Given 2.Corresp.  s post. 3.Def of   s 4.Def of  lines 5.Def of rt.  6.Substitution prop = 7.Def of rt.  8.Def of  lines

13. Ex: Find: m  1= m  2= m  3= m  4= m  5= m  6= x= 125 o 2 1 3 4 6 5 x+15 o

14. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Check It Out! Example 1 Find mQRS. mQRS = 180° – x x = 118 mQRS + x = 180° Corr. s Post. = 180° – 118° = 62° Subtract x from both sides. Substitute 118° for x. Def. of Linear Pair

15. Holt Geometry 3-2 Angles Formed by Parallel Lines and Transversals Find each angle measure. Example 2: Finding Angle Measures A. mEDG B. mBDG mEDG = 75°Alt. Ext. s Thm. mBDG = 105° x – 30° = 75° Alt. Ext. s Thm. x = 105Add 30 to both sides.

16. Assignment