Background Essay: Angles - Vertical and Congruent

When two lines lie on a flat surface, they are parallel or else they intersect at some point. Parallel lines never meet or intersect. They remain an equal distance apart no matter how far they are extended.

On the other hand, intersecting lines do cross. When intersecting lines cross, they form four pairs of supplementary angles. A supplementary angle is formed when the sum of the measures of two angles equals 180^o. At the intersection, the angles that lie diagonally opposite one another are called vertical angles. Vertical angles are always equal in measure. When angles are equal in measure, we say they are congruent.