Parallel Lines Assessment - Martinez, Teresa pd 4

In the picture above you will see that the GREEN lines, lines A and B, and parallel. This means that they can go on forever and never run into each other. Intersecting lines A and B is the PINK line, line C. This is the transversal. A transversal is a line that intersects two coplanar lines at two different points. One way we can prove that line A and line B are parallel is by using the 'Consecutive Interior Angles (Same-side Interior Angles) Theorem.' In this theorem we are just looking at the interior angles (<3,<4,<5, and <6). Basically if the two pairs of same-side interior angles (angles that lie in between the two parallel lines AND on the same side of the transversal) are supplementary, the you have proven the two lines are parallel.

In the picture above you will notice that the two lines running from left to right, labeled A and B, are parallel lines. This means they can run on forever and never run into each other. The line running up and down, intersecting them is line C. Line C is a transversal, a line that intersects two coplanar lines at two different points. One way we can prove that lines A and B are parallel is by using 'Converse of the Alternate Exterior Angles Theorem' which basically says that if two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel. A pair of alternate exterior angles (angles that lie on opposite sides of the transversal AND on the outside of the parallel lines) in this picture are <1 and <7. If the given to these angles were that angles 1 and 7 are both 120 degrees, then you would know that they are both equal, which makes them congruent. And if these angles are congruent then according to this theorem, lines A and B are parallel.