1. 4.5 I NTRO TO P ARALLEL L INES How can we recognize planes, transversals, pairs of angles formed by a transversal, and parallel lines?

2. D EFINITION : P ARALLEL L INES Two coplanar lines that do not intersect P LANE U NDEFINED T ERM : P LANE A surface such that if any two points on the surface are connected by a line, all points of the line are also on the surface. A plane only has 2 dimensions. Special Note: NON-Coplanar Lines are called Skew Lines

3. S YMBOLS FOR P ARALLEL L INES

4. R ECALL THE THREE UNDEFINED TERMS

5. D EFINITION : C OPLANAR Points, lines, and segments on the same plane. Definition: N ONCOPLANAR Points, lines, and segments not on the same plane.

6. A F B D G

7. D EFINITION : T RANSVERSAL A line that intersects two coplanar lines in two distinct points. T Note that the lines are not necessarily parallel.

8. D EFINITIONS : OF S PECIAL A NGLES 1 2 3 4 5 6 7 8 Interior Angles – lie between the two ll lines (  3,  4,  5, and  6) Alternate Interior Angles – are on opposite sides of the transversal. (  3 &  6 AND  4 and  5) Same-Side Interior Angles – are on the same side of the transversal. (  3 &  5 AND  4 &  6) T

9. 6 5 4 3 D EFINITIONS : M ORE S PECIAL A NGLES 2 1 7 8 Exterior Angles – lie outside the two lines (  1,  2,  7, and  8) Alternate Exterior Angles – are on opposite sides of the transversal (  1&  8 AND  2 &  7) Corresponding Angles – same location, different intersections (  2 &  6,  4 &  8,  1 &  5,  3 &  7)