Question

Prove that the straight lines perpendicular to the same straight line are parallel to one another.

Answer 1

The figure can be drawn as follows:

Here, and.

We need to prove that

It is given that , therefore,

(i)

Similarly, we have, therefore,

(ii)

From (i) and (ii), we get:

But these are the pair of corresponding angles.

Theorem states: If a transversal intersects two lines in such a way that a pair of corresponding angles is equal, then the two lines are parallel.

Thus, we can say that .