Perpendicular Lines Theorem

The Perpendicular Lines Theorem is a theorem which states that perpendicular lines, which by definition form one right angle, form four right angles.

Proof

To proof this, assume 2 lines which intersect at a point A to form four angles, 1, 2, 3, and 4. Angle 1 is right, because the lines are perpendicular. By the Straight Angle Theorem, angles the rays of which form a line are supplementary, and thus angle 1 and angles 2 and 4 are supplementary. By the definition of supplementary, the sum of the measures of each is 180^o and through simple algebra, the measure of each is 90^o. Similar logic is applied to the fourth to yield four right angles.