Introduction to Geometry: Parallel and Perpendicular Lines

Justification of Perpendicular Lines

Let's go through the justification of perpendicular lines.

Theorem
If two lines intersect, and one of the angles is 90°, then the lines are perpendicular.

line segment C D perpendicular to line segment S F, at point B, the angle made is 90 degrees

Justification
Two segments CD and SF intersect at B and one of the four angles formed around B is 90 degrees. Consider m angle CBS = 90°. Since angle CBS and angle FBD are vertical, then m angle FBD = 90°.

On the other hand, angle CBS and angle SBD are supplementary angles. Since m angle CBS = 90°, then its supplement, m angle SBD = 90°.

Similarly, angle FBD and angle CBF are supplementary. Thus, m angle CBF = 90°.

Having all angles around B with 90° measures, we conclude that CD and FS are perpendicular.