# Corresponding Angles

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 1 What are Corresponding Angles? 2 Corresponding Angles Formula 3 Corresponding Angles Types 4 Corresponding Angles Postulate 5 Important notes on Corresponding Angles 6 Solved Examples on Corresponding Angles 7 Challenging Questions on Corresponding Angles 8 Practice Questions on Corresponding Angles 9 Frequently Asked Questions (FAQs)

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## What are Corresponding Angles?

Let's begin this topic by first understanding the meaning of corresponding angles.

The Math definition for corresponding angles tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other. Applying the Math definition for corresponding angles, we can see that:

• Lines 1 and 2 are parallel. Thus, we have two parallel lines

• Line 3 is intersecting lines 1 and 2. Thus, we have intersected parallel lines

• From the diagram, we can see that angles 1 and 2 are occupying the same relative position - the upper right side angles in the intersection region.

It is clear that our Math definition for corresponding angles seems to be fulfilled.

Therefore, we can say that angles 1 and 2 are corresponding angles.

Now that we have understood the Math definition of corresponding angles, we can figure out whether any two given angles are corresponding or not in any given diagram.

Now, let us go a little deeper in to the meaning of corresponding angles.

The word “corresponding” itself suggests that the angles can be either analogous or equivalent (congruent).

Surprisingly, corresponding angles are considered to be analogous angles which are congruent.

Recalling our corresponding angles 1 and 2, we can tell that angles 1 and 2 are congruent.

## Corresponding Angles Formula

Using the corresponding angles in Math definition, we know how corresponding angles are found in a given diagram.

But, we can also interpret that there is no formula to define such angles.

We typically recognize corresponding angles by observing the diagram.

Hence, any two angles that satisfy the definition are said to be corresponding angles.

## Corresponding Angles Types

We know that each intersection point has 4 angles.

Now, each of the four angles in the first intersection region will have another one with the same relative position in the second intersection region.

Look at the simulation given here.

Click on any angle to know the other angle with the same relative position as the one you clicked.

Now, we will separate each of these four angles into different categories.

See the table below to get a better understanding of the different types of corresponding angles.

 Name of Angles Location Angles 1 and 5 Upper Right Side Angle Angles 2 and 6 Upper Left Side Angle Angles 3 and 7 Lower Right Side Angle Angles 4 and 8 Lower Left Side Angle

## Corresponding Angles Postulate

We already know that if a line intersects two parallel lines, then the corresponding angles in the two intersection regions are congruent.

But now, let's suppose that a line intersects two other lines (lines 1 and 2 that are not necessarily parallel).

Now the corresponding angles are found to be congruent.

Then, what can you say about the lines 1 and 2? Now, according to the postulate of corresponding angles, the statement “If a line intersects two parallel lines, then the corresponding angles in the two intersection regions are congruent” is true either way.

Thus, the converse of the statement would be, “If the corresponding angles in the two intersection regions are congruent, then the two lines are said to be parallel.”

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