Answer
The product of the slopes of two perpendicular lines is always -1.
Work Step by Step
We draw two triangles, both starting at the intersection of the two lines and both containing one vertical side. They share a vertical angle, so they have a congruent set of angles by the vertical angles theorem. Additionally, they both contain a right angle, which is congruent to itself by the vertical angles theorem. Finally, the triangles have congruent hypotenuses, so they are congruent by AAS. The rise of one triangle corresponds to the run of the other, and the run of that triangle corresponds to the negative rise of the other. Thus, when these two values are multiplied, the result is -1.
