1. Parallel Lines and Planes

2. Chapter 3 Parallel Lines and Planes page 72
Essential Question
How can you apply parallel lines (planes) to make deductions?

3. Lesson 3-1 Definitions (page 73)
Essential Question
How can you apply parallel lines (planes) to make deductions?

4. LINES
one
Intersecting Lines - intersection occurs at ________
point.

5. not l || m PARALLEL LINES ( ||-lines ) :
coplanar lines that do _______ intersect.
not l m
l || m

6. not 3. SKEW LINES : lines that are _____ coplanar.
r & t are skew lines

7. More SKEW LINES. y x
x & y are skew lines

8. PLANES
1. Intersecting Planes - intersection is a _______.
line

9. plane M & plane N are horizonal planes
PARALLEL PLANES ( ||-planes ) :
planes that do _______ intersect.
not
plane M || plane N
plane M & plane N are horizonal planes

10. LINE and PLANE
1. Line Contained in a Plane - every point on line is in the plane.

11. intersect Line Parallel to a Plane
- the line and plane do not _____________.
intersect

12. point 3. Line Intersects the Plane
- the intersection occurs at one (1) _______.
point

13. Theorem 3-1 Turn to page 74 Trace the diagram
If two parallel planes are cut by a third plane, then the lines are parallel.
Given: plane X || plane Y
plane Z intersects X in line l
plane Z intersects Y in line m
Prove: l || m Z
Turn to page 74
Trace the diagram
And copy the proof in your notes.

14. TRANSVERSAL: a line that intersects 2 or more coplanar lines in different points.1 4 3 m
t is a transversal 5 6 n 8 7 t
Figure A

15. TRANSVERSAL: a line that intersects 2 or more coplanar lines in different points.
z is a transversal 12 11 10 9 15 16 14 13 z y x
Figure B

16. Exterior angles: examples: ____________________________________∠1
; ∠2
; ∠7
; ∠8
exterior 2 1 4 3 m 5 6 n 8 7
exterior t
Figure A

17. Exterior angles: examples: ____________________________________∠9
; ∠12
; ∠13
; ∠16 e x t r i o e x t r i o 12 11 10 9 16 15 14 13 z y x
Figure B

18. Interior angles: examples: ____________________________________∠3
; ∠4
; ∠5
; ∠6 2 1 4 3 m
interior 5 6 n 8 7 t
Figure A

19. Interior angles: examples: ____________________________________
∠10
; ∠11
; ∠14
; ∠15 i n t e r o 11 12 10 9 15 16 14 13 z y x
Figure B

20. Alternate Interior Angles: 2 nonadjacent interior angles on opposite sides of the transversal. examples: ____________________________________ ∠3
and ∠5
; ∠4
and ∠6 2 1 4 3 m
interior 5 6 n 8 7 t
Figure A

21. Alternate Interior Angles: examples: ____________________________________
∠10
and ∠15
; ∠14
and ∠11 i n t e r o 11 12 10 9 15 16 14 13 z y x
Figure B

22. Same Side Interior Angles: 2 interior angles on same side of a transversal . examples: ____________________________________ ∠4
and ∠5
; ∠3
and ∠6 2 1 4 3 m
interior 5 6 n 8 7 t
Figure A

23. Same Side Interior Angles: examples: ____________________________________
∠10
and ∠11
; ∠14
and ∠15 i n t e r o 11 12 10 9 15 16 14 13 z y x
Figure B

24. Corresponding Angles: 2 angles in corresponding positions relative to 2 lines. examples: _______________________________________________
∠1 & ∠5
; ∠2 & ∠6
; ∠3 & ∠7
; ∠4 & ∠8 1 2 4 3 m 5 6 n 8 7 t
Figure A

25. Corresponding Angles: examples: _______________________________________________
∠9 & ∠11
; ∠10 & ∠12
; ∠13 & ∠15
; ∠14 & ∠16 11 12 10 9 15 16 14 13 z y x
Figure B

26. Transversals t m 1 2 9 10 3 4 n 11 12 p 14 13 6 5 16 15 8 7 18 17 19 20

27. Using transversal t, name angle pairs.1 2 9 10 3 4 n 11 12 p 14 13 6 5 16 15 8 7 18 17 19 20

28. Using transversal p, name angle pairs.1 2 9 10 3 4 n 11 12 p 14 13 6 5 16 15 8 7 18 17 19 20

29. How can you apply parallel lines (planes) to make deductions?
Assignment
Written Exercises on pages 76 & 77
RECOMMENDED: 1 to 17 odd numbers
REQUIRED: 23 to 41 odd numbers
How can you apply parallel lines (planes) to make deductions?