![]() This is an especially useful theorem for proving lines are parallel. ![]() The converse theorem tells us that if a transversal intersects two lines and the interior angles on the same side of the transversal are supplementary, then the lines are parallel. The converse of the Same Side Interior Angles Theorem is also true. Same Side Interior Angles Theorem – If a transversal intersects two parallel lines, then the interior angles on the same side of the transversal are supplementary.Ī transversal through two lines creates eight angles, four of which can be paired off as same side interior angles. Since either ∠ C or ∠ A can complete the equation, then ∠ C = ∠ A. We know two true statements from the theorem: Two theorems involve parallel lines.Ĭongruent Supplements Theorem - If two angles - we'll call them ∠ C and ∠ A - are both supplementary to a third angle (we'll call it ∠ T), then ∠ C and ∠ A are congruent. Supplementary angles are seen in three geometry theorems. The third set has three angles that sum to 180 ° three angles cannot be supplementary. Only those pairs are supplementary angles. Notice the only sets that sum to 180 ° are the first, fifth, sixth and eighth pairs. ![]() Identify the ones that are supplementary: Here are eight sets of angles in degrees.
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