How To Use Different External Angles To Create Parallel Lines?

Alternate exterior angles are pairs of non-adjacent angles on the outer sides of regions formed by intersecting parallel lines with a transversal line, positioned alternately. When two parallel lines are cut by a transversal at two distinct lines, the resulting alternate exterior angles are congruent. The term “alternate” means “alternating sides” of the transversal, and the name clearly describes the “location” of these angles.

The Alternate Exterior Angles Theorem states that when a transversal cuts two parallel lines, the pairs of exterior angles formed are congruent. In the figure below, transversal l intersects lines m and n forming 8 angles. The pairs are equal when the measures are equal when the lines are parallel.

To determine whether or not lines are parallel, students should use the alternate exterior angles theorem. Alternate exterior angles are those that are on opposite sides of the transversal but not adjacent and outside both parallel lines. If the alternate exterior angles formed by two lines, which are cut by a transversal, are congruent, then the lines are parallel.

To construct a line parallel to a given line that passes through a given point with a compass and straightedge or ruler, follow these steps:

1. Use your straightedge to draw a transversal through point P. This is a straight line that passes through P and intersects with a given line. If two lines and a transversal form alternate exterior angles that are congruent, then the lines are parallel.