Transversal
Transversal
Video: Parallel Lines, Transversals, and Angles
Transversals play a role in establishing whether two other lines in the Euclidean plane are parallel. The intersections of a transversal with two lines create various types of pairs of angles: consecutive interior angles, corresponding angles, and alternate angles. By Euclid's parallel postulate, if the two lines are parallel, consecutive interior angles are supplementary, corresponding angles are equal, and alternate angles are equal.
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| Eight angles of a transversal. (Vertical angles such as and are always congruent.) |
Transversal between non-parallel lines. Consecutive angles are not supplementary. |
Transversal between parallel lines. Consecutive angles are supplementary. |
and 
are always congruent.)Angles of a transversal
A transversal produces 8 angles, as shown in the graph at the above left:
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4 with each of the two lines, namely α, β, γ and δ and then α1, β1, γ1 and δ1; and
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4 of which are interior (between the two lines), namely α, β, γ1 and δ1 and 4 of which are exterior, namely α1, β1, γ and δ.
A transversal that cuts two parallel lines at right angles is called a perpendicular transversal. In this case, all 8 angles are right angles
When the lines are parallel, a case that is often considered, a transversal produces several congruent and several supplementary angles. Some of these angle pairs have specific names and are discussed below: corresponding angles, alternate angles, and consecutive angles.
Video: Figuring out angles between transversal and parallel lines
Corresponding angles
One pair of corresponding angles. With parallel lines, they are congruent.
Corresponding angles are the .......
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