In mathematics, particularly in geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects parallel lines, it creates several pairs of angles that have special relationships, such as corresponding angles, alternate interior angles, and same-side interior angles.
Here’s a brief overview of these types of angles formed when a transversal crosses parallel lines:
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Corresponding Angles: These are angles that are in the same position at each intersection. If the lines are parallel, corresponding angles are equal.
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Alternate Interior Angles: These are angles located on opposite sides of the transversal and between the two lines. If the lines are parallel, alternate interior angles are equal.
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Alternate Exterior Angles: These are located on opposite sides of the transversal but outside the two lines. If the lines are parallel, alternate exterior angles are equal.
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Same-Side Interior Angles: These are on the same side of the transversal and between the two lines. If the lines are parallel, these angles are supplementary, meaning they add up to 180 degrees.
Transversals are fundamental in proving various geometric properties and theorems related to parallel lines and angles.