1. WARM UP Look through pages 192-195 Write down the definitions of –Transversals –Interior –Exterior –Alternate Interior Angles –Alternate Exterior Angles –Corresponding Angles

2. 4.5 Parallel lines

3. Obj: recognize planes, Recognize transversals, identify the pairs of angles formed by a transversal, recognize parallel lines.

4. Plane: A surface with any two points connected by a line. There must be at least one point not on the line. Has only two dimensions, length and width (infinite) Has no thickness Plane m m y x

5. Coplanar: Points that lie on the same plane (like collinear) Non-coplanar: points that do not lie on the same plane

6. Transversals: A line that intersects two coplanar lines in two distinct points. Not always parallel. Parts of a transversal: Exterior region Interior region Exterior region

7. Transversals angles: alternate interior angles, angles on opposite sides of the transversal in the interior region alternate exterior angles, angles on opposite sides if the transversal in the exterior region

8. corresponding angles: angles in the same position in relation to the transversal

9. 1 2 3 4 5 6 7 8 Name the alternate interior angles. Name the alternate exterior angles. Name the corresponding angles.

10. 7 m n k 12 3 4 56 8 When the two lines cut by the transversal are parallel, certain angles are congruent! Given: lines n and m are parallel cut by transversal k

11. m n k 12 3 4 56 8 Alternate interior angles are congruent Alternate exterior angles are congruent Corresponding angles are congruent

12. m n k 12 3 4 56 8 Name the alternate interior angles Name the alternate exterior angles Name the corresponding angles What other angles are congruent???

13. Notice: if you know one angle in a set of transversal lines where two of the lines are parallel, you know all eight angles. Given: <1 = 45degrees, name the other angles. m n k 12 3 4 56 8

14. Parallel lines: two coplanar lines that do not intersect. (equidistance apart) symbol ll or on lines > > segments and rays can also be parallel to be parallel, the lines MUST BE COPLANAR!

15. Skew lines: Lines that never touch aren’t coplanar or parallel!