1. 3-1 Properties of Parallel Lines
L.E.Q. What special angles are created by two lines cut by a transversal and how are they related?

2. Remember: What would you call two lines which do not intersect?
Parallel
A solid arrow placed on two lines of a diagram indicate the lines are parallel.
The symbol || is used to indicate parallel lines.
AB || CD

3. What is a transversal?
A transversal is a line which intersects two or more lines in a plane. The intersected lines do not have to be parallel.
Lines j, k, and m are intersected by line t. Therefore, line t is a transversal of lines j, k, and m.

4. Pairs of Angles Formed By 2 Lines Cut By a Transversal

5. Alternate interior angles
Two nonadjacent interior angles on opp. Sides of the transversal
3 and 6
4 and 5

6. Same side interior angles
Two interior angles on the same side of the transversal
4 and 6
3 and 5

7. Corresponding angles 2 and 6 1 and 5 3 and 7 4 and 8
Two angles in corresponding position relative to the two lines
2 and 6
1 and 5
3 and 7
4 and 8

8. Which angle is the same side interior angle to D?A E F H C A B D C F E G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

9. Which angle is the alternate interior angle to D?A E F H C A B D C F E G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

10. Which angle is the corresponding angle to C?A E F H G A B D C F E G H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

11. Identifying Corresponding Angles
List all the sets of corresponding angles:
1&5, 2&6, 3&7, 4&8 t 1 2 3 4 5 6 7 8

12. Identifying Alternate Interior Angles
List all the sets of alternate interior angles:
3&6, 4&5 t 1 2 3 4 5 6 7 8

13. Identifying Same-Side Interior Angles
List all the sets of same-side interior angles:
3&5, 4&6 t 1 2 3 4 5 6 7 8

14. Corresponding Angles Postulate
If 2 parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2

15. Alternate Interior Angles Theorem
If 2 parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 3 4

16. Same-Side Interior Angles Theorem
If 2 parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary. 5 6

17. If angle 1 is 47 degrees find the following:
Can you determine the measure of specific angles with given information?
If angle 1 is 47 degrees find the following:
Angle 4
Angle 5
Angle 2
Angle 8

18. EXAMPLE: Using algebra to find angle measures.
Find the values of x and y. Then find the measures of the angles. 2x y
y - 50

19. Hw: pg #s 1-16 skip 9