The figure below shows a straight line ab intersected by another straight line t: a segment ab is intersected by a transversal labeled t. angles 1 and 3 and 2 and 4 are vertically opposite angles formed by the transversal on the segment. write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3.

When two straight lines intersect, the pairs of nonadjacent angles in opposite posi-tions are known as vertical angles.

If a segment AB is intersected by a transversal labeled t, then ∠1 and ∠3 and ∠2 and ∠4 are vertically angles formed by the transversal t on the segment AB.

Angles ∠1 and ∠2 can be described as adjacent and supplementary angles, so

.

Angles ∠3 and ∠2 can be also described as adjacent and supplementary angles, so

.

Subtract from the first equation the second equation:

.

Similarly you can prove that .