Alternate Exterior Angles Theorem
If two parallel lines are intersected by a transversal, then the alternate ecterior angles are congruent
The Alternate Exterior Angles Theorem is a geometric theorem used to relate the angles formed by a transversal cutting through two parallel lines. The theorem states that when two parallel lines are cut by a transversal, the pairs of alternate exterior angles are congruent (have the same measure).
In other words, if line l is parallel to line m, and transversal n cuts through both lines, then angle 1 and angle 8 (alternately exterior to lines l and m) are congruent, as are angles 2 and 7, angles 3 and 6, and angles 4 and 5.
This theorem is useful in a number of situations, particularly in geometry proofs involving parallel lines. For example, it can be used to prove that two lines are parallel by demonstrating that their alternate exterior angles are congruent. Additionally, it can be used to find angles in complex geometric figures.
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