1. Parallel Lines Lesson 4.5

2. Objective: Recognize planes and transversals, identify the pairs of angles formed by a transversal and recognize parallel lines.

3. 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

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

5. 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

6. 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. Corresponding Angles: angles in the same position in relation to the transversal.

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

8. 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

9. m n k 12 3 4 56 8 Alternate interior angles are congruent. Alternate exterior angles are congruent. Corresponding angles are congruent. 7

10. 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??? 7

11. 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 = 45°name the other angles. m n k 12 3 4 56 8 7

12. 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!

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