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If a transversal line meets two lines, eight angles are formed at the points of intersection as shown in the Figure-1.
Figure-1
It is clear that the pairs of angles \(∠1, ∠2\), ; \(∠3, ∠4,\) ; \(∠5, ∠6\)and \(∠7, ∠8\) are linear pairs.
Besides, the pairs \(∠1, ∠3\) ; \(∠2, ∠4\) ; \(∠5, ∠7\ \)and \(∠6, ∠8\) are vertically opposite angles.
We can further classify the angles into different categories as follows:
Corresponding angles:
Figure-2
Observe that the pair of angles \(∠1\) and \(∠5\) that are marked at the right side of the transversal line \(l\). In that \(∠1\) lies above the line \(m\) and \(∠5\) lies above the line \(n\).
Also observe the pair of angles \(∠2\) and \(∠6\)that are marked on the left of the transversal line \(l\). In that \(∠2\ \)lies above \(m\) and \(∠6\ \)lies above \(n\).
In the same way observe the pair of angles \(∠3\) and \(∠7\) that are marked on left of transversal line \(l\). In that \(∠3\) lies below \(m\) and \(∠7\) lies below \(n\).
Observe the pair of angles \(∠4\) and \(∠8\) that are marked on the right of transversal line \(l\). In that \(∠4\)lies below \(m\) and \(∠8\) lies below \(n\).
So all these pairs of angles have different vertices, lie on the same side (left or right) of the transversal line (\(l\)) lie above or below the lines \(m\) and \(n\). Such pairs are called corresponding angles.
Alternate Interior angles
Figure-3
Each of pair of angles named \(∠3\) and \(∠5\), \(∠4\) and \(∠6\) are marked on the opposite side of the transversal line \(l\) and are lying between lines \(m\) and \(n\) are called alternate interior angles.
Alternate Exterior angles
Figure-4
Each pair of angles named \(∠1\) and \(∠7\), \(∠2\) and \(∠8\) are marked on the opposite side of the transversal line \(l\) and are lying outside of the lines \(m\) and \(n\) are called alternate exterior angles.
Some more pairs of angles.
Figure-5
> Each pair of angles named \(∠3\) and \(∠6\), \(∠4\) and \(∠5\) are marked on the same side of transversal line \(l\) and are lying between the lines \(m\) and \(n\). These angles are lying on the interior of the lines \(m\) and \(n\) as well as the same side of the transversal line \(l\). Called as co-interior angles.
Figure-6
> Each pair of angles named \(∠1\) and \(∠8\), \(∠2\) and \(∠7\ \)are marked on the same side of transversal line \(l\) and are lying outside of the lines \(m\) and \(n\). These angles are lying on the exterior of the lines \(m\) and \(n\) as well as the same side of the transversal line \(l\). Called as co-exterior angles.
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