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Angle relationships formed by parallel lines
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A transversal is a line that intersects two or more lines.
When a transversal crosses parallel lines, special angle relationships form.
Corresponding Angles: Same position at each intersection
Alternate Interior Angles: Between the parallel lines, opposite sides
Alternate Exterior Angles: Outside the parallel lines, opposite sides
Consecutive Interior Angles (Same-Side Interior): Between parallel lines, same side
Two parallel lines are cut by a transversal. If one angle measures , what is the measure of its corresponding angle?
Corresponding angles are congruent when lines are parallel.
Answer:
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If two parallel lines are cut by a transversal:
If these angle relationships hold, then the lines are parallel.
Parallel lines and are cut by a transversal. Two consecutive interior angles measure and . Find .
Consecutive interior angles are supplementary.
Lines and are cut by transversal . Alternate interior angles measure and . Are lines and parallel?
For the lines to be parallel, alternate interior angles must be congruent.
Set them equal:
Answer:
When :
Since the angles are equal, the lines are parallel.
Answer: Yes, the lines are parallel