2. Section 3.1 Lines and Angles Standards #7 & 16 Thursday, June 30, 2016Thursday, June 30, 2016Thursday, June 30, 2016Thursday, June 30, 2016

3. Goals 1. Identify relationships between lines 2. Identify angles formed by transversals

4. Lines in the same plane that never intersect. AB and CD are parallel lines Parallel lines A B C D

5. Planes that never intersect. Planes U and W are parallel Parallel Planes wu

6. Skew Lines Lines that never intersect and are not parallel. AB and CD are skew lines. C D A B

7. Transversal A line that intersects two or more coplanar lines at different points. m n w w is a transversal

8. Corresponding Angles (C.A.’s) Angles that occupy a similar position when two lines are cut by a transversal. (4 pairs) 1 2  1 and  2 are corresponding angles. (They are congruent if the lines are parallel.)

9. Alternate Exterior Angles (A.E.A.’s) Angles who lie on the outside the two lines on opposite sides of the transversal. (2 pairs) 3 4  3 and  4 are alternate exterior angles. (They are congruent if the lines are parallel.)

10. Alternate Interior Angles (A.I.A.’s) Two angles who lie between the two lines on opposite sides of the transversal. (2 pairs) 5 6  5 and  6 are alternate interior angles. (They are congruent if the 2 lines are parallel.)

11. Two angles that lie between the lines on the same side of the transversal. (2 pairs) Consecutive Interior Angles (C.I.A.’s) 7 8  7 and  8 are consecutive interior angles. (They are supplementary if the 2 lines are parallel.)

12. Example #1 Which line… a.is parallel to and contains V? b.is perpend. to and contains V? c.is skew to and contains V? T P Q R V W U S

13. Answers to #1 1)UV 2)VW 3)RV, SV T P Q R V W U S

14. Example #2 List all pairs of angles that fit the description. A Corresponding (C.A.)(4) B Alternate Exterior (A.E.A.)(2) C. Alternate Interior (A.I.A.)(2) D. Consecutive Interior(C.I.A.)(2) 6 51 2 3 4 7 8

15. Answers to #2 A.<1 & <3, <5 & <7, <2 & <4, <6 & <8 B.<1 & <8, <5 & <4 C.<2 & <7, <6 & <3 D.<2 & <3, <6 & <7 6 51 2 3 4 7 8

16. SUMMARY Now, take the next few minutes to write your summary. Make sure that you have at least 3 complete sentences…

17. Assignment Pages 132 #10-31, 48-62 even(2-column algebra proofs)

18. Assignment 3.1 HW Pages 132 #3-17, 21-26 48-56