1. Parallel Lines and Transversals
Chapter 3-1

2. Lesson 3-1 Ideas/Vocabulary
Identify the relationships between two lines or two planes.
Name angles formed by a pair of lines and a transversal.
parallel lines
consecutive interior angles
alternate exterior angles
alternate interior angles
corresponding angles
parallel planes
skew lines
transversal
Preparation for Standard 7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key)
Lesson 3-1 Ideas/Vocabulary

3. Triangles are used to indicate // lines
Parallel Lines //
Two lines are // if they are coplanar and do not intersect.
Triangles are used to indicate // lines

4. Skew Lines
Lines that do not intersect but are not coplanar are called skew lines.

5. Parallel Planes
Two planes that do not intersect.

6. Based on looks, find a line:
// to AB and containing D
 to AB and containing D
Skew to AB and containing D
Name the plane(s) that contain D and appear to be // to plane ABE
1. DC A D E H B C G F
2. AD
4. DCH or DGH or DCG
3. DH

7. Identify Relationships
A. Name all planes that are parallel to plane AEF.
Answer: plane BHG
Lesson 3-1 Example 1a

8. Identify Relationships__
B. Name all segments that intersect AF.
Answer: EF, GF, DA, and BA __
Lesson 3-1 Example 1b

9. Identify Relationships__
C. Name all segments that are skew to AD.
Answer: FG, GB, EH, EC, and CH __
Lesson 3-1 Example 1c

10. A. Name a plane that is parallel to plane RST.B C D
plane WTZ
plane SYZ
plane WXY
plane QRX
Lesson 3-1 CYP 1a

11. B. Name a segment that intersects YZ.XY WX QW RS A. B. C. D.
Lesson 3-1 CYP 1b

12. C. Name a segment that is parallel to RX.B. C. D. ZW TZ QR ST
Lesson 3-1 CYP 1c

13. D. Name a segment that is skew to TZ. __RX ST XW QW __
___ A B C D
Lesson 3-1 CYP 1d

14. Transversal
A line that intersects two or more coplanar lines at different points. t 1 2 3 4 5 6 7 8
t is a transversal

15. If the lines are extended, line v intersects lines u, w, x, and z.
Identify Transversals
A. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line v is a transversal.
Answer:
If the lines are extended, line v intersects lines u, w, x, and z.
Lesson 3-1 Example 2a

16. Identify Transversals
B. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line y is a transversal.
Answer:
lines u, w, x, z
Lesson 3-1 Example 2b

17. Identify Transversals
C. BUS STATION Some of a bus station’s driveways are shown. Identify the sets of lines to which line u is a transversal.
Answer:
lines v, x, y, z
Lesson 3-1 Example 2c

18. A. HIKING A group of nature trails is shown
A. HIKING A group of nature trails is shown. Identify the sets of lines to which line a is a transversal. A B C D
lines c, f
lines c, d, e
lines c, d, f
lines c, d, e, f
Lesson 3-1 CYP 2a

19. B. HIKING A group of nature trails is shown
B. HIKING A group of nature trails is shown. Identify the sets of lines to which line b is a transversal. A B C D
no lines
lines c, f
lines c, d, e, f
lines a, c, d, e, f
Lesson 3-1 CYP 2b

20. C. HIKING A group of nature trails is shown
C. HIKING A group of nature trails is shown. Identify the sets of lines to which line c is a transversal. A B C D
lines a, b
lines a, b, d, e, f
lines a, d, f
lines a, b, e
Lesson 3-1 CYP 2c

21. D. HIKING A group of nature trails is shown
D. HIKING A group of nature trails is shown. Identify the sets of lines to which line d is a transversal. A B C D
lines e, f
lines a, b, f
lines a, b, c, e, f
lines a, b, c
Lesson 3-1 CYP 2d

22. Corresponding Angles Two angles that occupy corresponding positions. t
1 and 5 are corresponding s t 1 2 3 4 5 6 7 8
2 and 6 are corresponding s
3 and 7 are corresponding s
4 and 8 are corresponding s

23. Alternate Interior Angles
Two angles that lie between the two lines on opposite sides of the transversal. t 1 2 3 4 5 6 7 8
3 and 6 are Alt. Int. s
4 and 5 are Alt. Int. s

24. Alternate Exterior Angles
Two angles that lie outside the two lines on opposite sides of the transversal. t 1 2 3 4 5 6 7 8
1 and 8 are Alt. Ext. s
2 and 7 are Alt. Ext. s

25. Consecutive Interior Angles
Two angles that lie between the two lines on the same side of the transversal. t 1 2 3 4 5 6 7 8
3 and 5 are Consecutive Int. s
4 and 6 are Consecutive Int. s
Sometimes called Same Side Interior Angles

26. Identify Angle Relationships
A. Identify 7 and 3 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
corresponding
Lesson 3-1 Example 3a

27. Identify Angle Relationships
B. Identify 8 and 2 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
alternate exterior
Lesson 3-1 Example 3b

28. Identify Angle Relationships
C. Identify 4 and as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
corresponding
Lesson 3-1 Example 3c

29. Identify Angle Relationships
D. Identify 7 and 1 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
alternate exterior
Lesson 3-1 Example 3d

30. Identify Angle Relationships
E. Identify 3 and 9 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
alternate interior
Lesson 3-1 Example 3e

31. Identify Angle Relationships
F. Identify 7 and as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
Answer:
consecutive interior
Lesson 3-1 Example 3f

32. A. Identify 4 and 5. A B C D alternate interior alternate exterior
corresponding
consecutive interior
Lesson 3-1 CYP 3a

33. B. Identify 7 and 9. A B C D alternate interior alternate exterior
corresponding
consecutive interior
Lesson 3-1 CYP 3b

34. C. Identify 4 and 7. A B C D alternate interior alternate exterior
corresponding
consecutive interior
Lesson 3-1 CYP 3c

35. D. Identify 2 and 11. A B C D alternate interior alternate exterior
corresponding
consecutive interior
Lesson 3-1 CYP 3d

36. E. Identify 3 and 5. A B C D alternate interior alternate exterior
corresponding
consecutive interior
Lesson 3-1 CYP 3e

37. F. Identify 6 and 9. A B C D alternate interior alternate exterior
corresponding
consecutive interior
Lesson 3-1 CYP 3e

38. Practice 1 4 3 2 8 5 6 7 11 9 10 12

39. Homework
pg. 144
12-19,
24-35,
41-44