Transversals

We saw what happens when two lines intersect in different ways. Let us explore what happens when one line intersects two different lines.

In the figure, line t intersects lines l and m. t is called a transversal. Notice that angles are formed when a line crosses a pair of lines.

Is it possible for all the eight angles to have different measurements? Why, why not? YesNo

The angles will have different measurements only if the lines l and m are not parallel.

What about five different angles: 6, 5, 4, 3 and 2? 2 and are vertically opposite angles; 5 and as well as 3 with and 4 are supplementary angles.

In the figure, since ∠1 and ∠ are vertically opposite angles, they are .

Are there other pairs of vertically opposite angles? We can see that there are a total of pairs of vertically opposite angles and in each pair, the angles are to each other.

Thus, when a transversal intersects two lines, it forms eight angles with a maximum of four distinct angle measures.