Theorem 3-4 Same-Side Exterior Angles Theorem
If a transversal intersects two parallel lines, then same-side exterior angles are supplementary
The Same-Side Exterior Angles Theorem states that for any given pair of parallel lines cut by a transversal line, the exterior angles that are on the same side of the transversal are congruent.
In other words, if line l and m are parallel and line n is transversal to both lines, and if angle 1 and angle 2 are both exterior angles on the same side of the transversal line n, then angle 1 is congruent to angle 2, or ∠1 ≅ ∠2.
This theorem can be proven using the corresponding angles postulate, which states that when two parallel lines are cut by a transversal, the corresponding angles are congruent. Since the exterior angles are supplementary to the corresponding interior angles, and since congruent angles have the same measure, we can conclude that the same-side exterior angles are congruent.
The Same-Side Exterior Angles Theorem is useful in solving various types of geometric problems, such as finding missing angles in intersecting lines or angles in polygons. It can also be used to prove other theorems, such as the Triangle Sum Theorem.
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