Corresponding Angles

Corresponding angles are formed when two parallel lines are intersected by a third line called the transversal. In the figure below, the parallel lines k and l are intersected by the transversal line t:

The four pairs of corresponding angles are:

∠1 and ∠5

∠2 and ∠6

∠3 and ∠7

∠4 and ∠8

They are corresponding angles because they occupy the same relative position.

Corresponding angles postulate

The corresponding angles postulate says when two parallel lines are intersected by a transversal, the resulting corresponding angles are congruent.

Let's take a look at the following figure:

According to the corresponding angles postulate, if l and m are parallel (l ∥ m) and intersected by the transversal n, then ∠1 and ∠2 are congruent $∠1 ≅ ∠2$ .

The converse of this statement is also true. If l and m are intersected by a transversal in such a way that the corresponding angles formed are congruent, then l ∥ m.

Exterior and interior angles

For each pair of corresponding angles, one angle is an exterior angle and the other is an interior angle. For example, ∠1 is an exterior angle because it falls outside of the parallel lines, while ∠5 is an interior angle because it rests between the parallel lines:

Alternate, consecutive, and vertical angles

While corresponding angles fall on the same side of the transversal, alternate angles fall on opposite sides of the transversal. For example, ∠4 and ∠6 are alternate angles:

Since ∠4 and ∠6 are also exterior angles, they are called alternate exterior angles, while ∠3 and ∠5 are alternate interior angles.

Like corresponding angles, consecutive angles fall on the same side of the transversal. Consecutive interior angles are both inside of the parallel lines (ex. ∠2 and ∠5), while consecutive exterior angles are both outside of the parallel lines (ex. ∠4 and ∠7).

In the above figure, you can also see vertical angles, which are a pair of opposites formed by intersecting lines (ex. ∠1 and ∠3).

Corresponding angles in polygons

Corresponding angles can also be found in similar and congruent polygons. For example, take a look at the following similar pentagons:

In the figure, ∠A and ∠V are corresponding angles. So are ∠C and ∠X.

Practice questions on corresponding angles

a. In the above figure, what is the transversal?

Line n

b. In the above figure, which lines are parallel?

Lines l and m

c. In the above figure, what are ∠1 and ∠2?

Corresponding angles

d. In the above figure, what are ∠2 and ∠4?

Vertical angles

e. In the above figure, what are ∠1 and ∠7?

Alternate exterior angles

f. In the above figure, what are ∠3 and ∠8?

Consecutive interior angles

g. In the above figure, what are ∠2 and ∠8?

Alternate interior angles

Topics related to the Corresponding Angles

Parallel Lines and Transversals

Angle-Angle Similarity

Congruent Figures

Flashcards covering the Corresponding Angles

Advanced Geometry Flashcards

Common Core: High School - Geometry Flashcards

Practice tests covering the Corresponding Angles

Common Core: High School - Geometry Diagnostic Tests

Advanced Geometry Diagnostic Tests

Get help learning about corresponding angles

If your student is just being introduced to angles, whether they're corresponding, consecutive, alternate, or vertical, they might have a difficult time identifying them, particularly when exterior and interior angles are included. If your student is having trouble with angles or would like to improve their knowledge while working on an assignment or preparing for a test, tutoring can help. Speak with the Educational Directors at Varsity Tutors today to learn about the perks of having your student work with a tutor.