Transversal

A line which intersects two or more lines at distinct points is called a transversal. When a transversal intersects two lines, eight angles are formed.

These angles in pairs are very important in the study of properties of parallel lines.

Angles of Transversal

∠1 and ∠5 is a pair of corresponding angles. ∠2 and ∠6, ∠3 and ∠7 and ∠4 and ∠8 are other pairs of corresponding angles.

∠3 and ∠6 is a pair of alternate angles. ∠4 and ∠5 is another pair of alternate angles.

∠3 and ∠5 is a pair of interior angles on the same side of the transversal. ∠4 and ∠6 is another pair of interior angles.

Transversal and Parallel Lines

When a transversal intersects two parallel lines, then angles in

each pair of corresponding angles are equal

∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7 and ∠4 = ∠8

each pair of alternate angles are equal

∠3 = ∠6 and ∠4 = ∠5

each pair of interior angles on the same side of the transversal are supplementary

∠3 + ∠5 = 180° and ∠4 + ∠6 = 180°

Equal Intercept Theorem

A line which intersects two or more lines is called a transversal. The line segment cut off from the transversal by a pair of lines is called an intercept.

If there are three or more parallel lines and the intercepts made by them on a transversal are equal, the corresponding intercepts made on any other transversal are also equal.