What happens when parallel lines are cut by transversals? What are the different types of angles formed by the crossing of lines? On this page you will learn to identify angle pairs, relationships, and their properties using concepts from parallel lines cut by transversals.
When a transversal crosses parallel lines, different angles are formed. These angles can be corresponding angles (angles in the same spot at each intersection), vertical angles (opposite), alternate interior angles ( inside angles in alternate spots), alternate exterior angles (outside angles in alternate spots) and consecutive interior angles. .
Corresponding angles (angles in the same spot at each intersection)
These are angles formed that occupy the same relative position at each intersection when a transversal crosses other parallel lines.
Corresponding angles theorem:
Angles formed by a transversal that intersects parallel lines are congruent.
Above image shows that parallel lines CD and EF are transversed by line AB, where:
∠l = ∠l5, ∠2 = ∠l8, ∠3 = ∠l6, and ∠4 = ∠l7
Note: Corresponding angles can be supplementary if the transversal intersects two parallel lines perpendicularly at right angles then each of the corresponding angles will be 90 degrees and their sum will add up to 180 degrees.
Types of corresponding angles:
Corresponding interior angle:
Angle formed at the inner side of the intersection between the parallel lines and the transversal.
∠4, ∠2, ∠5, and ∠6
Corresponding exterior angle:
Angle formed at the outer side of the intersection between the parallel lines and the transversal.
∠1, ∠3, ∠7, and ∠8
Vertical angles
Vertical angles, sometimes called opposite angles, are opposite each other in two intersecting lines. According to the vertical angle theorem, vertical angles are always congruent angles therefore their angle measurements are also the same.
From the given image we can spot some examples of vertical angles:
∠l and ∠2, ∠3 and ∠4, ∠5 and ∠8, and ∠6 and ∠7.
Alternate interior angles
These are pairs of angles on the inner side of each of those two lines but on opposite sides of the transversal.
From the given image we can spot some examples of alternate interior angles:
∠4 and ∠6, and ∠2 and ∠5.
Alternate exterior angles
These are pairs of angles on the outer side of each of those two lines but on opposite sides of the transversal.
From the given image we can spot some examples of alternate exterior angles:
∠1 and ∠8, and ∠3 and ∠7.
Consecutive interior angles
These are pairs of angles on one side of the transversal and inside the two lines.
From the given image we can spot some examples of consecutive interior angles:
∠2 and ∠6, and ∠4 and ∠5.
Conclusion
When a transversal cuts parallel lines, five angle types can be formed. First is the corresponding angles or the angles formed at the same relative position at each intersection. Next is the vertical angles or the angles created opposite at each other through a transversal. Then we have the alternate interior angles or the angles on the inner side of each of those two lines but on opposite sides of the transversal. We also have the alternate exterior angles formed at the outside of the two parallel lines with a transversal.Lastly, we have the consecutive interior angles or angles on one side of the transversal and inside the two lines. These angles are supplementary to each other which add up to 180 degrees.