3.1 Lines and Angles

Parallel Lines

Alternative Definitions: Parallel Lines – lines that have the same slope (algebra 1) Parallel Lines – 2 lines in which the distance between the two lines is always constant (never changing). To think about this idea imagine a ladder or set of railroad tracks. The rungs of the ladder are always the same length and the railroad ties are always the same length.

Parallel lines have no points in common. NO INTERSECTION. Any two lines that do intersect must be coplanar. The intersection of two lines is always either a single point or infinite points. If two lines were parallel last year you would solve a system and get a false statement like 3=7 or -1=4 for example. This meant you had NO SOLUTIONS In order to have two lines intersect infinite times the two lines must be on top of one another. The geometric word for this is that the lines must COINCIDE. Algebraically last year you would find that whenever you use a system of equations and ended up getting a true statement like 10=10 or -3=-3 for example it told you that you had infinite solutions.

Skew Lines

Think about skewers in cooking/grilling. Why are they called that?

Parallel Planes

Line t is a transversal here. Lines l and m are not transversals. Transversal - A line that intersects two or more coplanar lines at distinct (different) points. Line t is a transversal here. Lines l and m are not transversals. Angles 3, 4, 5, 6 are referred to as INTERIOR ANGLES because they are between or on the inside of lines l and m. Angles 1, 2, 8, 7 are referred to as EXTERIOR ANGLES because they are on the outsides of lines l and m.

HWK MathXL 3.1