a transversal
A transversal is simply a line that crosses two or more other lines. Think of a railway crossing where one road cuts straight across a pair of parallel rails: the road is the transversal, slicing through both rails and making a cluster of angles at each crossing. The word just means 'crossing line'.
Precisely: if a line t meets line m at one point and line n at a different point, then t is a transversal of m and n. At each of the two crossings, t makes four angles, so altogether there are eight angles. These eight come in named families according to where they sit: corresponding angles (same position at each crossing), alternate interior angles (between the two lines, on opposite sides of t), alternate exterior angles (outside the two lines, on opposite sides of t), and co-interior angles (between the two lines, on the same side of t). The transversal is the stage on which all the parallel-line angle relationships are played out.
The transversal idea matters because it is the setup for the parallel-lines criterion: only when m and n are parallel do those angle families satisfy their tidy equalities and supplements. If m and n are not parallel, a transversal still creates all eight angles, but the corresponding pairs need not be equal — so the angle relationships are a test for parallelism, not an automatic gift.
Draw two horizontal lines, then a slanted line cutting through both. That slanted line is a transversal; you will see four angles where it meets the top line and four where it meets the bottom, eight in all.
A transversal crosses two lines and creates eight angles in named families.
A transversal need not be perpendicular and the two crossed lines need not be parallel; 'transversal' only describes a line that crosses them at two distinct points.