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What is the meaning of transversal? What are the angles made by a transversal?
Transversal lines:
When a line intersects two lines at distinct points, it is called a transversal.
In the figure below, the line p intersects lines l and m at two distinct points.
Therefore, line p is the transversal line.
.
Vertically Opposite Angles:
When two lines intersect, we get four angles. The angles are two pairs of opposite angels and those angles are known as vertically opposite angles.
In the above figure, ∠1, ∠3 and ∠4, ∠2 are vertically opposite angles.
When a transversal intersects two lines, it forms a different kind of angles.
Interior Angles:
The angles formed in between the lines P and Q are called interior angles.
In the above figure, ∠3, ∠4 and ∠6, ∠5 are present in between the lines, so they are interior angles.
Exterior Angles:
The angles that are formed outside the lines P and Q are called exterior angles.
In the above figure, ∠1, ∠2 and ∠7, ∠8 are present exterior to the lines, so they are exterior angles.
Pairs of Corresponding angles:
Angles in corresponding positions related to the two lines are called pairs of corresponding angles.
In the above figure, (∠1, ∠5), (∠2, ∠6), (∠3, ∠7) and (∠4, ∠8) are pairs of corresponding angles.
Pairs of Alternate Interior Angles:
In the interior angles ∠3, ∠4, ∠5, and ∠6, the angles (∠3, ∠5) and (∠4, ∠6) are at alternate positions. Hence, they are known as pairs of alternate interior angles.
In these pairs of alternate interior angles, the angles have different vertices and the angles lie ‘between’ the two lines but on either side of the transversal.
Pairs of Alternate Exterior Angles:
In exterior angles ∠1, ∠7, ∠2 and ∠8, two pairs of angles which are (∠1, ∠7) and (∠2, ∠8) are at alternate positions, thus they are known as pairs of alternate exterior angles.
Pairs of Interior Angles on the Same Side of Transversal:
In the interior angles ∠3, ∠4, ∠5 and ∠6, the angles (∠4, ∠5) and (∠3, ∠6) are pairs of interior angles on the same side of the transversal.
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