1. 3-1 Parallel Lines and Transversals

2. CCSS Content Standards
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.

3. Then/Now
You used angle and line segment relationships to prove theorems.
Identify relationships between two lines or two planes.
Name angle pairs formed by parallel lines and transversals.

4. Vocabulary parallel lines skew lines parallel planes transversal
interior angles
exterior angles
consecutive interior angles
alternate interior angles
alternate exterior angles
corresponding angles

5. Concept

6. Vocabulary transversal:
a line that intersects two or more coplanar lines at two different points

7. Example 1
A. Name all segments parallel to BC.
Answer: AD, EH, FG

8. Example 1
B. Name a segment skew to EH.
Answer: AB, CD, BG, or CF

9. Example 1
C. Name a plane parallel to plane ABG.
Answer: plane CDE

10. Example 1a A. Name a plane that is parallel to plane RST. A. plane WTZ
B. plane SYZ
C. plane WXY
D. plane QRX

11. Example 1b B. Name a segment that intersects YZ. A. XY B. WX C. QW
D. RS

12. Example 1c C. Name a segment that is parallel to RX. A. ZW B. TZ C. QR
D. ST

13. Concept

14. Vocabulary
Interior angles
Example:

15. Vocabulary
Exterior angles
Example:

16. Vocabulary
Consecutive interior angles
Example:

17. Vocabulary
Alternate interior angles
Example:

18. Vocabulary
Alternate exterior angles
Example:

19. Vocabulary
Corresponding angles
Example:

20. Example 2
A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: corresponding

21. Example 2
B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: alternate exterior

22. Example 2
C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: consecutive interior

23. Example 2
D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer: alternate interior

24. Example 2a A. Classify the relationship between 4 and 5.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior

25. Example 2b B. Classify the relationship between 7 and 9.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior

26. Example 2c C. Classify the relationship between 4 and 7.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior

27. Example 2d D. Classify the relationship between 2 and 11.
A. alternate interior
B. alternate exterior
C. corresponding
D. consecutive interior

28. Example 3
A. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 1 and 2. Then classify the relationship between the pair of angles.
Answer: The transversal connecting 1 and 2 is line v. These are corresponding angles.

29. Example 3
B. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 2 and 3. Then classify the relationship between the pair of angles.
Answer: The transversal connecting 2 and 3 is line v. These are alternate interior angles.

30. Example 3
C. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 4 and 5. Then classify the relationship between the pair of angles.
Answer: The transversal connecting 4 and 5 is line y. These are consecutive interior angles.