Proving Parallel Lines
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Videos, worksheets, games and activities to help PreCalculus students learn how to use the converse of the parallel lines theorem to prove that lines are parallel.
What is the corresponding angle postulate?
If two parallel lines are cut by a transversal then the pairs of corresponding angles are congruent.
What is the corresponding angle converse?
If two lines are cut by a transversal such that the corresponding angles are congruent then the lines are parallel.
What is the alternate interior angles theorem?
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
What is the alternate interior angles converse?
If two lines are cut by a transversal such that the pairs of alternate interior angles are congruent, then the lines are parallel.
What is the alternate exterior angles theorem?
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
What is the alternate exterior angles converse?
If two parallel lines are cut by a transversal such that the pairs of alternate exterior angles are congruent, then the lines are parallel.
What is the consecutive interior angles theorem?
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
What is the consecutive interior angles converse?
If two lines are cut by a transversal such that the consecutive interior angles are supplementary then the lines are parallel.
What is the transitive property of parallel lines?
If two lines are parallel to the same line, then they are parallel to each other.
Converse of Parallel Lines Theorem
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.
Proving Lines Parallel; topics: Converse of the Corresponding Angles Theorem, Converse of the Alternate Interior Angles Theorem, Converse of the Same-Side Interior Angles Postulate, Converse of the Alternate Exterior Angles Theorem and applying this.
Students learn the converse of the parallel line postulate. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel. Students are then asked to determine which lines are parallel in given figures using information about the angles in the figures.
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