Basics of Corresponding Angles.

The Cambridge Dictionary defines corresponding angles to be two equal angles on the same side of a line that crosses two parallel lines and on the same side of each parallel line. Our need to know how to determine the values of corresponding angles is applicable to most fields of endeavor, from architectural design and construction to navigation aids such as radar to locate ships and airplanes. But how do you go about finding the values for corresponding angles?

Park Seo Jun and Park Min Young in What's Wrong With Secretary Kim (2018).

The Theorem of Corresponding Angles
The theorem of corresponding angles states that if two parallel lines are intersected by a transversal line, then the pairs of corresponding angles formed are congruent. A transversal line is a line that passes through two other lines. Corresponding angles are those angles that are in the same relative position at the intersections of a transversal line and two parallel lines. Note that the two lines must always be parallel for this theorem to apply.

How to Find Corresponding Angles
According to the Corresponding Angle Postulate, when a transversal line intersects two parallel lines, all of the corresponding angles must be equal. Thus, if you know the value of one of the corresponding angles, then you know that the other corresponding angle is equal to it. In addition, because a straight line forms a straight angle, which measures 180 degrees, you can also determine the value of the angle adjacent to the known angle by subtracting the known value from 180.

How to Know When Lines are Parallel
According to the converse of the Corresponding Angle Postulate, if two lines and a transversal line form corresponding angles that are congruent, then the two lines are parallel. If the lines were not parallel, a triangle would be formed between the transversal and the point where the two other lines intersect. In this case, the corresponding angles would have no specific relationship to each other, and geometry could be used to determine the value of each of the angles. (Parallel lines are identified by two arrowheads or two small lines for each parallel line.)

Yoo Seung Ho and Chae Soo Bin in I Am Not A Robot (2017).

The Need to Know Corresponding Angles
Everything around us forms lines and angles. From the books we read to the homes and buildings we occupy to the roads on which we drive, it all comes down to lines and angles. Most of our cities are laid out in grid patterns of lines and angles. We use maps and GPS as navigation aids, whether we are driving, flying, or sailing the seas. We even walk in straight lines and angles. Surely, it makes sense that we know the relationship between lines and angles.

Thus, the value of knowing how to find corresponding angles reaches out to us in ways we might not always comprehend, from the simplest gestures to the most complex algorithms. With a little awareness and enough practice, maybe we can begin to recognize the corresponding angles that appear in our own lives. Who knows? Maybe we can even apply that knowledge to improve our lives.