# How do you prove corresponding angles?

##### 1 Answer

The proof is based on the *Fifth Postulate of Euclid*.

See below.

#### Explanation:

Let

Two *one-sided* angles (on one side of transverse *interior* or *inner* (between the parallels) and another *exterior* (outside of the area between the parallel lines), are called *corresponding*.

So, angles

Take into account that sum of measures of *supplemental* angles

That is,

Now, if the *corresponding* angles *inner* angles

There are two cases, both mean that a sum of some pair of *inner* angles measure less than

*inner* angles' measures is less than

Let's recall the *Fifth Postulate of Euclid*.

If two lines on a plane intersect a third line in such a way that the sum of the inner angles on one side is less than two right angles, then the two lines inevitably must intersect each other on that side if extended far enough.

Therefore, since