1. Triangles and Lines – Angles and Lines When two lines intersect they create angles. Some special relationships occur when the lines have properties such as being parallel. Lines a and b are parallel. a b

2. Triangles and Lines – Angles and Lines When two lines intersect they create angles. Some special relationships occur when the lines have properties such as being parallel. Lines a and b are parallel. A transversal is a line that intersects these lines. a b

3. Triangles and Lines – Angles and Lines When two lines intersect they create angles. Some special relationships occur when the lines have properties such as being parallel. Lines a and b are parallel. A transversal is a line that intersects these lines. When it does, it creates eight angles… a b 1 2 34 5 6 7 8

4. Triangles and Lines – Angles and Lines When two lines intersect they create angles. Some special relationships occur when the lines have properties such as being parallel. Lines a and b are parallel. A transversal is a line that intersects these lines. Corresponding Angles are angles that are on the same side of the transversal and in the same position with respect to the parallel lines. Angles 1 and 5 are corresponding angles. These angles are also congruent. a b 1 2 34 5 6 7 8

5. Triangles and Lines – Angles and Lines When two lines intersect they create angles. Some special relationships occur when the lines have properties such as being parallel. Lines a and b are parallel. A transversal is a line that intersects these lines. Corresponding Angles are angles that are on the same side of the transversal and in the same position with respect to the parallel lines. Angles 1 and 5 are corresponding angles. These angles are also congruent. a b 1 2 34 5 6 7 8 Name another pair of corresponding angles that are congruent.

6. Triangles and Lines – Angles and Lines When two lines intersect they create angles. Some special relationships occur when the lines have properties such as being parallel. Lines a and b are parallel. A transversal is a line that intersects these lines. Corresponding Angles are angles that are on the same side of the transversal and in the same position with respect to the parallel lines. Angles 1 and 5 are corresponding angles. These angles are also congruent. a b 1 2 34 5 6 7 8 Name another pair of corresponding angles that are congruent. You could have named 2 & 6, 3 & 7, or 4 & 8…

7. Triangles and Lines – Angles and Lines Theorem : If two parallel lines are cut by a transversal, corresponding angles are congruent. a b 1 2 34 5 6 7 8

8. Triangles and Lines – Angles and Lines Theorem : If two parallel lines are cut by a transversal, corresponding angles are congruent. a b 1 2 34 5 6 7 8

9. Triangles and Lines – Angles and Lines Alternate angles – angles on opposite sides of the transversal. Angles 1 and 4 are alternate angles. a b 1 2 34 5 6 7 8

10. Triangles and Lines – Angles and Lines Alternate angles – angles on opposite sides of the transversal. Angles 1 and 4 are alternate angles. Name another pair of alternate angles… a b 1 2 34 5 6 7 8

11. Triangles and Lines – Angles and Lines Alternate angles – angles on opposite sides of the transversal. Angles 1 and 4 are alternate angles. Name another pair of alternate angles… You could have chosen 2 & 3, 5 & 8, 6 & 7… a b 1 2 34 5 6 7 8

12. Triangles and Lines – Angles and Lines Alternate angles – angles on opposite sides of the transversal. Angles 1 and 4 are alternate angles. Alternate Interior Angles – angles on opposite sides of the transversal and inside the parallel lines. a b 1 2 34 5 6 7 8

13. Triangles and Lines – Angles and Lines Alternate angles – angles on opposite sides of the transversal. Angles 1 and 4 are alternate angles. Alternate Interior Angles – angles on opposite sides of the transversal and inside the parallel lines. Angles 2 & 7, and 4 & 5 are alternate interior angles. a b 1 2 34 5 6 7 8 2 7 4 5

14. Triangles and Lines – Angles and Lines Alternate angles – angles on opposite sides of the transversal. Angles 1 and 4 are alternate angles. Alternate Interior Angles – angles on opposite sides of the transversal and inside the parallel lines. Angles 2 & 7, and 4 & 5 are alternate interior angles. Alternate Exterior Angles – angles on opposite sides of the transversal and outside the parallel lines. a b 1 2 34 5 6 7 8

15. Triangles and Lines – Angles and Lines Alternate angles – angles on opposite sides of the transversal. Angles 1 and 4 are alternate angles. Alternate Interior Angles – angles on opposite sides of the transversal and inside the parallel lines. Angles 2 & 7, and 4 & 5 are alternate interior angles. Alternate Exterior Angles – angles on opposite sides of the transversal and outside the parallel lines. a b 1 2 34 5 6 7 8 Angles 1 & 8, and angles 3 & 6 are Alternate Exterior Angles

16. Triangles and Lines – Angles and Lines Let’s take a look at some typical problems using these properties. a b 1 2 34 5 6 7 8 Example #1 :

17. Triangles and Lines – Angles and Lines Let’s take a look at some typical problems using these properties. a b 1 2 34 5 6 7 8 Example #1 : Angle #4 = 120° - they are alternate angles Angle #8 = 120° - they are alternate exterior angles Angle #5 = 120° - they are corresponding angles

18. Triangles and Lines – Angles and Lines Let’s take a look at some typical problems using these properties. a b 1 2 34 5 6 7 8 Example #1 :

19. Triangles and Lines – Angles and Lines Let’s take a look at some typical problems using these properties. a b 1 2 34 5 6 7 8 Example #1 : Angle #6 = 65° - they are alternate angles Angle #2 = 65° - they are alternate exterior angles Angle #3 = 65° - they are corresponding angles

20. Triangles and Lines – Angles and Lines Theorem - if two parallel lines are cut by a transversal, interior angles on the SAME side of the transversal are supplementary. a b 1 2 34 5 6 7 8

21. Triangles and Lines – Angles and Lines Theorem - if two parallel lines are cut by a transversal, interior angles on the SAME side of the transversal are supplementary. a b 1 2 34 5 6 7 8

22. Triangles and Lines – Angles and Lines Theorem - if two parallel lines are cut by a transversal, interior angles on the SAME side of the transversal are supplementary. a b 1 2 34 5 6 7 8 EXAMPLE :

23. Triangles and Lines – Angles and Lines Theorem - if two parallel lines are cut by a transversal, interior angles on the SAME side of the transversal are supplementary. a b 1 2 34 5 6 7 8 EXAMPLE :

24. Triangles and Lines – Angles and Lines Theorem - if two parallel lines are cut by a transversal, interior angles on the SAME side of the transversal are supplementary. a b 1 2 34 5 6 7 8 EXAMPLE # 2 :

25. Triangles and Lines – Angles and Lines Theorem - if two parallel lines are cut by a transversal, interior angles on the SAME side of the transversal are supplementary. a b 1 2 34 5 6 7 8 EXAMPLE # 2 :

26. Triangles and Lines – Angles and Lines Theorem - if two parallel lines are cut by a transversal, interior angles on the SAME side of the transversal are supplementary. a b 1 2 34 5 6 7 8 EXAMPLE # 2 : Since angles 1 & 4 are alternate angles and congruent, angle 1 = 120°