Alternate exterior
angles that are on opposite sides of the transversal and outside of the parallel lines
Alternate exterior angles are pairs of angles that are formed by two parallel lines and a transversal line that intersects both lines. These angles are located on opposite sides of the transversal line and on the exterior of the parallel lines.
In other words, if we have two parallel lines and a third line (called a transversal) intersects those parallel lines at some point, then the alternate exterior angles are the pairs of angles that are on opposite sides of the transversal and outside of the parallel lines.
The main property of alternate exterior angles is that they are congruent to each other. That is, if we have two alternate exterior angles, then they will always have the same measure.
For example, in the figure below, lines l and m are parallel, and line n is a transversal. Angles 1 and 8 represent a pair of alternate exterior angles, as do angles 3 and 6:
“`
/\
/ \
/____\
1
|
|
3—-+—–6
|
|
8
“`
Since lines l and m are parallel, we know that angles 1 and 3, as well as angles 6 and 8, are corresponding angles and are thus congruent. Similarly, since angles 1 and 8 are alternate exterior angles, they are also congruent.
Overall, alternate exterior angles are an important concept in geometry and can be used to prove many useful theorems about parallel lines and transversals.
More Answers:
The Foundational Concepts Of Geometry: Points, Lines, And PlanesThe Corresponding Angles Postulate: Key Concepts In Geometry
Same-Side Interior Angles And Their Special Relationship.