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Corresponding Angles

Definition: Corresponding angles are the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line (i.e. the transversal). For example, in the below-given figure, angle p and angle w are the corresponding angles.

corresponding_angles
Corresponding Angles Examples and Types

Examples of the corresponding angle are any angles which are formed on the opposite side of the transversal. Now, it should be noted that the transversal can intersect either two parallel lines or two non-parallel lines. Thus, corresponding angles can be of two types:

Here we will discuss only corresponding angles formed by the intersection of two lines by a transversal. The two lines could be parallel or non-parallel. So, let us learn corresponding angles for both the cases.

Corresponding Angles Formed by Parallel Lines and Transversals:

If a line or a transversal crosses any two given parallel lines, then the corresponding angles formed have equal measure. In the given figure, you can see, the two parallel lines are intersected by a transversal, which forms eight angles with the transversal. So, the angles formed by the first line with the transversal have equal corresponding angles formed by the second line with the transversal.

Angles formed by parallel lines and transversal

All corresponding angle pairs in the figure:

Note:

Corresponding Angles Formed by Non-Parallel Lines and Transversals:

For non-parallel lines, if a transversal intersects them, then the corresponding angles formed doesn’t have any relation with each other. They are not equal as in the case of parallel lines but all are corresponding to each other.

Angles formed by non-parallel lines and transversal
Corresponding Angles Theorem

According to the corresponding angles theorem, the statement “If a line intersects two parallel lines, then the corresponding angles are congruent (equal)” is true either way. This theorem is also termed as "corresponding angles postulate".

Diagram showing corresponding angles theorem
The Converse of Corresponding Angles Theorem

The corresponding angles converse theorem would be, “If the corresponding angles are congruent, then the two lines are said to be parallel.”

What if a transversal intersects two lines and the pair of corresponding angles are equal? Then, the two lines intersected by the transversal are said to be parallel. This is the converse of the corresponding angle theorem.

Important Notes on Corresponding Angles:


Square Root

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