Parallel Lines

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Parallel lines are lines that are coplanar (lie in the same plane) and do not intersect each other, no matter how far they are extended. They maintain a constant distance between them. Symbol: ∥

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A transversal is a line that intersects two or more lines at distinct points. When a transversal crosses two parallel lines, it creates eight angles with special relationships.

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When a transversal intersects two parallel lines creating angles 1, 2, 3, 4 on the first line and 5, 6, 7, 8 on the second line, the corresponding angle pairs are: (∠1, ∠5), (∠2, ∠6), (∠3, ∠7), (∠4, ∠

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Alternate interior angles are pairs of angles that are on opposite sides of the transversal and inside (between) the two parallel lines. Example pairs: if angles are numbered 1-8, then (∠3, ∠6) and (∠

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Alternate exterior angles are pairs of angles that are on opposite sides of the transversal and outside the two parallel lines. These angles are not between the parallel lines but beyond them on alter

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Co-interior angles (or interior angles on the same side of the transversal) are pairs of angles that are on the same side of the transversal and between the two parallel lines. These angles are supple

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Interior Angle Theorem: If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are supplementary (their sum is 180°). This means ∠a + ∠b =

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Corresponding Angles Theorem: When two parallel lines are cut by a transversal, corresponding angles are equal in measure. If lines are parallel, then all pairs of corresponding angles are congruent (