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Corresponding Angles

What Are equivalent Angles?

A corresponding angle is one the holds the exact same relative position as an additional angle elsewhere in the figure. Equivalent angles in aircraft geometry are produced when transversals cross 2 lines.

You are watching: Converse of the corresponding angles theorem


Two angles correspond or relate to each various other by gift on the very same side of the transversal. One is one exterior angle (outside the parallel lines), and one is one interior angle (inside the parallel lines).


Corresponding angle are simply one kind of edge pair. Angles that room on the opposite next of the transversal space called alternative angles. You have the right to have alternate interior angles and alternative exterior angles.

Corresponding angles are never surrounding angles. They perform not touch, for this reason they can never be consecutive inner angles.

Which angles Are matching Angles?

Can you uncover the equivalent angle for angle 2 in our figure?


Did you an alert angle 6 coincides to angle 2? They room a pair of corresponding angles. Deserve to you discover all four matching pairs of angles?

Here space the four pairs of corresponding angles:

Angles 1 and 5Angles 2 and 6Angles 3 and also 7Angles 4 and also 8

Corresponding angles Theorem

When a transversal line crosses two lines, eight angles space formed. The Corresponding angles Theorem claims that:

The corresponding Angles Postulate is simple, but it packs a beat because, v it, friend can create relationships for every eight angles of the figure.


Because of the equivalent Angles Theorem, you currently know number of things about the eight angles produced by the three lines:If one is a right angle, every are appropriate anglesIf one is acute, four are acute anglesIf one is obtuse, four are obtuse anglesAll eight angles have the right to be divide as nearby angles, upright angles, and corresponding angles


If you have a 2 parallel lines reduced by a transversal, and one angle (angle 2) is labeled 57°, making that acute, ours theroem tells us that there room three various other acute angles are formed.

The angles to either side of our 57° edge – the adjacent angles – are obtuse. The edge opposite angle 2, angle 3, is a vertical angle come angle 2. They share a vertex and also are opposite every other.

The converse of the equivalent Angles organize is also interesting:

The converse theorem allows you to evaluate a figure quickly. If girlfriend are given a figure comparable to our figure below, yet with only two angle labeled, have the right to you determine anything by it?


Since the corresponding angles are presented to be congruent, you recognize that the 2 lines reduced by the transversal room parallel.

If the lines cut by the transversal space not parallel, then the matching angles are not equal. They space just matching by location.

Corresponding angle Examples

Looking at our BOLD MATH figure again, and thinking of the equivalent Angles Theorem, if you understand that angle 1 actions 123°, what various other angle must have actually the very same measure?You deserve to use the matching Angles Theorem even without a drawing. If two corresponding angles the a transversal across parallel lines are right angles, what execute you know around the figure?Can girlfriend possibly attract parallel lines v a transversal that creates a pair of matching angles, each measuring 181°?Imagine a transversal cutting throughout two lines. You find out that matching angles room not congruent. What does that tell you around the lines cut by the transversal?

And now, the answers (try your best first!):

Angle 5 additionally measures 123°. Since of the vertical angle theorem, angle 4 and 8 additionally measure 123°.If two matching angles the a transversal across parallel currently are appropriate angles, all angle are right angles, and also the transversal is perpendicular come the parallel lines.You cannot possibly attract parallel lines with a transversal that creates a pair of corresponding angles, every measuring 181°.With transversal cutting throughout two lines forming non-congruent matching angles, you know that the 2 lines room not parallel.

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Next Lesson:

Angle Relationships

What you learned:

After functioning your means through this lesson and also video, you have learned:

The definition of corresponding AnglesCorresponding angle TheoremWhen a transversal crossed 2 parallel lines, the corresponding angles space equal.When a transversal crossed two non-parallel lines, the matching angles are not equal.