1. Parallel Lines and Planes
Chapter 3

2. Section 3-3

3. Theorem
If two lines are cut by a transversal and alternate exterior angles are congruent, then the lines are parallel.
Which angles must be congruent to prove lines r and s are parallel?

4. Postulate
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.
Which angles need to be congruent in order for lines r and s to be parallel?

5. Theorem
If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.
If <4 is congruent to <6 (or <3 is congruent to <5), then lines r and s are parallel.

6. Theorem
If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.
Which angles must be supplementary to prove lines r and s are parallel?

7. Ways to Show Lines are Parallel
Show a pair of corresponding angles are congruent
Show a pair of alternate interior angles are congruent
Show a pair of same-side interior angles are supplementary
In a plane, show that both lines are perpendicular to a third line
Show that both lines are parallel to a third line

8. Homework- Proving Lines Parallel
3-3 Practice Worksheet (7-17 all)

9. Proof PPT

10. Section 3-4 p.164

11. Theorem
If two parallel planes are cut by a third plane, then the lines of intersection are parallel
Examples:
Floor and ceiling intersected by a wall

12. Theorem
If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other one also. (Perpendicular Transversal Theorem)

13. Theorem
In a plane, two lines perpendicular to the same line are parallel.
If line t is perpendicular to line k and line t is also perpendicular to line l, then lines l and k are parallel.

14. If two lines are parallel to the same line, then they are parallel to each other.

15. Section 3-5 p.171

16. More Theorems
Through a point not on a line, there is exactly one line parallel to the given line.
Through a point not on a line, there is exactly one line perpendicular to the given line.

17. Triangle Angle Sum Theorem
The sum of the measures of the angles of a triangle is 180.

18. Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

19. Ratio of Angles in a Triangle
The ratio of the angles in a triangle is 2:3:4
What are the measures of the three angles?
2x + 3x + 4x = 180
x = 20
40°, 60°, and 80°

20. Homework
p #2, 7
p #9, 12-14, 17, 20, 22-24