Draw the two non vertical lines.

Let $\"\"$ and $\"\"$ are the slopes of two lines.

Consider the points $\"\"$ is on the line and its slope is $\"\"$ .

The point $\"\"$ is on the line and its slope is $\"\"$ .

Consider the lines are perpendicular.

Then $\"\"$ is a triangle.

Apply converse of Pythagorean theorem :

If $\"\"$ , then $\"\"$ is a right triangle.

$\"\"$

$\"\"$ .

$\"\"$ is a right triangle.

Therefore, If two lines are perpendicular then their slopes are negative reciprocals to each other.

If two non vertical lines have slopes whose product is $\"\"$ then the lines are perpendicular.