Angles, Interior and
Corresponding Angles, Parallel
|Two cars pass each other, going in opposite directions on separate and parallel
roadways. A crazy driver breaks through all the guard rails and narrowly misses
the other two drivers, Pip and Porter. Fortunately, Pip and Porter are outstanding
math students, and once their hearts stopped pounding, they analyzed the situation.
They first noticed that the crazy driver creates a transversal, which is a line
that intersects two parallel lines. The situation looks like this:
|Supplementary angles are angles that form a linear pair (add
up to 180 degrees). Examples of supplementary angles are angles 1 and 3, 1 and
2, 2 and 4, 3 and 4, etc.
Corresponding angles are angles that are in the same relative
position that the two parallel lines make with the transversal. Examples of corresponding
angles are angles 2 and 6, 1 and 5, etc. These angles have the same measure.
Exterior angles are angles that are on the outside of the parallel
lines that are cut by the transversal. Examples of exterior angles are angles
2 and 8, 1 and 7. These pairs add up to 180 degrees.
Interior angles are the angles formed on one side of the transversal
that cuts the parallel lines. Angles 4 and 6 as well as angles 3 and 5 are interior
angles. These pairs add up to 180 degrees.
The parallel lines property creates the above relationships. The Parallel Lines
Property states that if two lines are cut by a transversal such that alternate
interior or exterior angles have equal measure, then the two lines are parallel.
It also states that two lines cut by a transversal are parallel if and only if
corresponding angles have the same measure.