1. Unit 2: Properties of Angles and Triangles

2. 2.2 Angles Formed by Parallel Lines
Remember: When a transversal intersects a pair of parallel lines, the corresponding angles that are formed by each parallel line and the transversal are equal
Also, vertically opposite angles are equal

3. There are also other relationships among the measures of the eight angles formed when a transversal intersects two parallel lines.
Lets investigate the other angles

4. Alternate interior angles: two non-adjacent interior angles on opposite sides of a transversal.
Non adjacent = not beside each other

5. Since we know corresponding angles are equal when two parallel lines are intersected by a transversal and vertically opposite angles are equal, make a conjecture about alternate interior angles

7. Alternate exterior angles: two non-adjacent exterior angles formed between two lines and a transversal, on opposite sides of the transversal.

8. Since we know corresponding angles are equal when two parallel lines are intersected by a transversal, vertically opposite angles are equal AND alternate interior angles are equal, make a conjecture about alternate exterior angles
Let’s prove it!

9. Make a conjecture
Is there a relationship between two interior angles on the same side of the transversal?

11. Example 2 (p. 76)
Using reasoning, determine the measures of a, b, c, and d. Explain WHY!! Use your words!!

12. Example 3 (p. 77)

13. Example 20a (p.82)

14. Key Ideas When a transversal intersects two parallel lines,
The corresponding angles are equal
The alternate interior angles are equal
The alternate exterior angles are equal
The interior angles on the same side of the transversal are supplementary (add to 180°)

15. Need to know If a transversal intersects two lines such that
The corresponding angles are equal, or
The alternate interior angles are equal, or
The alternate exterior angles are equal, or
The interior angles on the same side of the transversal are supplementary
Then the lines are parallel

16. Homework P. 78-82 For extra practice for Quiz 2.1 and 2.2
# 1, 2, 3, 4, 8 (the upside down T means perpendicular) 10, 15, 16, 20b
For extra practice for Quiz 2.1 and 2.2
Mid chapter review p