Transversal

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In developing the geometry of parallel lines, observe the three lines arrangement 'l', 'm' and 't'.

In the diagram 'l' and 'm' are coplanar. They may be parallel as in figure 't' intersects 'l' and 'm' at two distinct points 'A' and 'B' and at 'C' and 'D'. Line t is called a transversal.

A transversal is a line that intersects (or cuts) two or more coplanar lines at distinct points.

Angles formed by a transversal

In the diagram and are two coplanar lines. PQRS is a transversal intersecting at Q and at R. Eight angles are formed, they are numbered from 1 to 8. By virtue of their locations, some of the angles can be paired together. The paired angles are given special names (apart from adjacent angles and vertical angles).

Interior angles on the same side of the transversal

Alternate angles

A pair of angles are said to be alternate angles if

(i) both are interior angles

(ii) they are on the opposite sides of the transversal and

(iii) they are not adjacent angles.

Alternate angles are some times also called alternate interior angles.

In the diagram,

Corresponding angles

A pair of angles are said to be corresponding angles if

one is an interior angle and the other is an exterior angle

they are on the same side of the transversal and

they are not adjacent angles.

The four pairs of corresponding angles are given below.