Section 2.6: Special Angle Relationships and Parallel Lines
Corresponding angles can apply to either two polygons or parallel lines cut by a transversal. In both cases, corresponding angles are in the same position. If the two polygons are congruent, then the corresponding angles are also congruent. If the two lines are parallel, then the corresponding angles created by the transversal are congruent.
Alternate interior angles are formed by a transversal intersecting two parallel lines . They are located between the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate interior angles. Alternate interior angles are congruent, meaning they have equal measure
Alternate exterior angles are formed by a transversal intersecting two parallel lines . They are located "outside" the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate exterior angles. Alternate exterior angles are congruent, meaning they have equal measure.
When two parallel lines are intersected by a transversal, same side interior (between the parallel lines) and same side exterior (outside the parallel lines) angles are formed. Since alternate interior and alternate exterior angles are congruent and since linear pairs of angles are supplementary, same side angles are supplementary.
If two lines are intersected by a transversal, then alternate interior angles, alternate exterior angles, and corresponding angles are congruent. The converse of the theorem is true as well. If two corresponding angles are congruent, then the two lines cut by the transversal must be parallel. Similarly, if two alternate interior or alternate exterior angles are congruent, the lines are parallel.
Alternate interior angles are formed by a transversal intersecting two parallel lines . They are located between the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate interior angles. Alternate interior angles are congruent, meaning they have equal measure
Alternate exterior angles are formed by a transversal intersecting two parallel lines . They are located "outside" the two parallel lines but on opposite sides of the transversal, creating two pairs (four total angles) of alternate exterior angles. Alternate exterior angles are congruent, meaning they have equal measure.
When two parallel lines are intersected by a transversal, same side interior (between the parallel lines) and same side exterior (outside the parallel lines) angles are formed. Since alternate interior and alternate exterior angles are congruent and since linear pairs of angles are supplementary, same side angles are supplementary.
If two lines are intersected by a transversal, then alternate interior angles, alternate exterior angles, and corresponding angles are congruent. The converse of the theorem is true as well. If two corresponding angles are congruent, then the two lines cut by the transversal must be parallel. Similarly, if two alternate interior or alternate exterior angles are congruent, the lines are parallel.
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