Corresponding Angles

Corresponding Angles: When two lines are intersected by any other line,(called transversal), the angles formed in matching corners or corresponding corners with the transversal are called as corresponding angles. For example, in the below-given figure, angle p and angle w are the corresponding angles.

corresponding angles

In Maths, you must have learned about different types of lines and angles. But here we will discuss only about 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 For Parallel Lines

If a line or we can say 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 transversal have equal corresponding angles formed by the second line with the transversal.

Corresponding angles for Parallel Lines

So, ∠p = ∠w

∠q= ∠x

∠r = ∠y

And ∠s = ∠z

You should also note down, apart from corresponding angles, there are other angles formed when a transversal intersects two parallel lines. These angles are;

Vertically Opposite angles

The angles formed opposite to each other by a transversal.

∠p = ∠s, ∠q = ∠r, ∠w = ∠ z and ∠x = ∠y

Alternate Interior Angles

The angles formed at the interior side or inside of the two parallel lines with a transversal.

∠r = ∠x and ∠s = ∠w

Alternate Exterior Angles

The angles formed at the outside or exterior side of the two parallel lines with a transversal.

∠p = ∠z and ∠q = ∠y

Consecutive Interior Angles/Co-interior Angles

The angles formed inside the two parallel lines but one side of the transversal is the consecutive interior angles. The angles are supplementary to each other, that means the sum of these two angles is 180°. Therefore,

∠r + ∠w = 180°

And ∠s + ∠x = 180°

Corresponding Angles For Non-Parallel Lines

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.

Corresponding Angles For Non-Parallel Lines

In the same, there is no relationship between the interior angles, exterior angles, vertically opposite angles and consecutive angles, in the case of the intersection of two non-parallel lines by a transversal.

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