2. 3-1 Properties of Parallel lines

3. Two or more lines are parallel if and only if they are in the same plane and they do not intersect. (line w and r) Two or more lines are parallel if and only if they are in the same plane and they do not intersect. (line w and r) lw lr lr || lw

4. Two figures that have the exact same size and shape (example: two angles that have the same measurement are congruent) Two figures that have the exact same size and shape (example: two angles that have the same measurement are congruent) lw lr = 122 Degrees lr || lw

5. A line intersecting two or more coplanar lines. (lines r and w) A line intersecting two or more coplanar lines. (lines r and w) lr lw lr || lw

6. If two parallel lines are cut by a transversal, then …… If two parallel lines are cut by a transversal, then …… Corresponding angles are congruent, Corresponding angles are congruent, Alternate Interior angles are congruent,.... And.... Alternate Interior angles are congruent,.... And.... Alternate Exterior angles are congruent. Alternate Exterior angles are congruent. Same-Side Interior Angles are supplementray Same-Side Interior Angles are supplementray lw lr4 1 3 2 56 78 5 1 5 4 1 8

7. If two parallel lines are cut by a transversal, then Corresponding angles are congruent. If two parallel lines are cut by a transversal, then Corresponding angles are congruent. 1 5 2 6 3 7 4 8 lr lw lr || lw

8. If two angles are Vertical angles, then they are also congruent. If two angles are Vertical angles, then they are also congruent. 1 4 2 3 5 8 7 6 lw lr lr || lw

9. If two parallel lines are cut by a transversal, then Alternate Exterior angles are congruent. If two parallel lines are cut by a transversal, then Alternate Exterior angles are congruent. 1 8 2 7 lw lr lr || lw

10. If two parallel lines are cut by a transversal, then Alternate Interior angles are congruent. If two parallel lines are cut by a transversal, then Alternate Interior angles are congruent. 3 6 4 5 lw lr lr || lw

12. angle 1 = 58 ˚angle 4 = 58 ˚angle 5 = 58 ˚angle 8 = 58 ˚ vertical angles Since angle 1 = 58 ˚ then angle 4 = 58 ˚ and since angle 5 = 58 ˚ then angle 8 = 58 ˚ because they are vertical angles, which are congruent to each other angle 1 = 58 ˚angle 5 = 58 ˚corresponding angles If angle 1 = 58 ˚ then angle 5 = 58 ˚ because they are corresponding angles, which are congruent to each other lr lw lr || lw 2 34 65 78 58 ˚ 58˚ 58˚

13. lr lw lr || lw 2 34 65 78 58 ˚ 122 122˚ 122˚ 122 ˚ angle 1 = 58 ˚angle 2 = 122 ˚line If angle 1 = 58 ˚ then angle 2 = 122 ˚ because the two angles form a line, which is equal to 180 ˚ angle 3 = 122 ˚angle 6 = 122 ˚Alternate Interior angles Since angle 3 = 122 ˚ then angle 6 = 122 ˚ because they are Alternate Interior angles, which are congruent to each other. angle 2 = 122 ˚angle 7 = 122 ˚Alternate Exterior angles Since angle 2 = 122 ˚ then angle 7 = 122 ˚ because they are Alternate Exterior angles, which are congruent to each other.

14. Compass Clipart from Microsoft Office Compass Clipart from Microsoft Office All other animals – pictures created by Michelle A. O’Malley All other animals – pictures created by Michelle A. O’Malley Serra, Michael. Discovering Geometry. Berkeley: Key Curriculum Press, 1997. Serra, Michael. Discovering Geometry. Berkeley: Key Curriculum Press, 1997.