Are these ratios equivalent?
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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 .