Parallel lines, transversals and polygon angles

A transversal makes eight angles

A transversal is a line that crosses two other lines. It creates eight angles, and certain pairs have names:

• corresponding angles: in the same position at each intersection (both "upper right", for example);
• alternate interior angles: between the two lines, on opposite sides of the transversal;
• alternate exterior angles: outside the two lines, on opposite sides of the transversal;
• same-side interior angles (also called consecutive interior angles): between the two lines, on the same side of the transversal.

When the lines are parallel

The first statement is usually taken as a postulate; the others follow from it using vertical angles and linear pairs.

Proving lines are parallel

Each statement above has a converse, and the converses are how you prove lines are parallel.

Angles of polygons

Draw every diagonal from one vertex of a convex polygon with \(n\) sides. You get \(n - 2\) triangles, whose angles together make up exactly the polygon's angles.

In a regular polygon all angles are congruent, so each exterior angle measures \(\frac{360°}{n}\) and each interior angle measures \(180°\) minus that. A regular nonagon has exterior angles of \(40°\) and interior angles of \(140°\).

Practice