Fundamental Ideas
Parallel Lines
A
transversal is any line that intersects two or more lines in the same plane but at different points. In Figure
1 , line
t is a transversal.
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A transversal that intersects two lines forms eight angles; certain pairs of these angles are given special names. They are as follows:
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Corresponding angles are the angles that appear to be in the same relative position in each group of four angles. In Figure 2 , ∠l and ∠5 are corresponding angles. Other pairs of corresponding angles in Figure 2 are: ∠4 and ∠8, ∠2 and ∠6, and ∠3 and ∠7.
Figure 2 A transversal intersecting two lines and forming various pairs of corresponding angles—alternate interior angles, alternate exterior angles, consecutive interior angles, and consecutive exterior angles.
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Alternate interior angles are angles within the lines being intersected, on opposite sides of the transversal, and are not adjacent. In Figure 2 , ∠4 and ∠6 are alternate interior angles. Also, ∠3 and ∠5 are alternate interior angles.
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Alternate exterior angles are angles outside the lines being intersected, on opposite sides of the transversal, and are not adjacent. In Figure 2 , ∠l and ∠7 are alternate exterior angles. Also, ∠2 and ∠8 are alternate exterior angles.
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Consecutive interior angles (same-side interior angles) are interior angles on the same side of the transversal. In Figure 2 , ∠4 and ∠5 are consecutive interior angles. Also, ∠3 and ∠6 are consecutive interior angles.
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Consecutive exterior angles (same-side exterior angles) are exterior angles on the same side of the transversal. In Figure 2 , ∠l and ∠8 are consecutive exterior angles. Also, ∠2 and ∠7 are consecutive exterior angles.
