SINCE both the lines are perpendicular on same line and they will make 90degree . so ,then sum of interoir angle will be 180 degree.Hence in this way it will be proved

Proof:

To prove that two lines perpendicular to the same line are parallel to each other, we need to understand the properties of perpendicular lines and parallel lines.

Perpendicular lines:
Two lines are said to be perpendicular if they intersect at a right angle (90 degrees). In other words, the slopes of the lines are negative reciprocals of each other.

Parallel lines:
Two lines are said to be parallel if they do not intersect and have the same slope. They have a constant distance between them.

Understanding the problem:
Let's assume we have a line m. We need to prove that if line A is perpendicular to line m and line B is also perpendicular to line m, then line A and line B are parallel to each other.

Proof:
We can prove this statement using contradiction.

Assume that line A and line B are not parallel to each other. This means that they intersect at some point, let's call it point C.

Now, since line A is perpendicular to line m, the angle formed by line A and line m at point C is 90 degrees. Similarly, since line B is perpendicular to line m, the angle formed by line B and line m at point C is also 90 degrees.

If line A and line B intersect at point C, then the angles formed by line A and line B at point C must add up to 180 degrees (straight angle). However, we know that both angles are 90 degrees, so their sum would be 180 degrees.

This contradicts the fact that the angles formed by line A and line B at point C add up to 180 degrees. Therefore, our assumption that line A and line B are not parallel is false.

Hence, we can conclude that if line A is perpendicular to line m and line B is also perpendicular to line m, then line A and line B are parallel to each other.