More Lessons for PreCalculus

Math Worksheets

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.

If two parallel lines are cut by a transversal then the pairs of corresponding angles are congruent.

If two lines are cut by a transversal such that the corresponding angles are congruent then the lines are parallel.

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

If two lines are cut by a transversal such that the pairs of alternate interior angles are congruent, then the lines are parallel.

If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.

If two parallel lines are cut by a transversal such that the pairs of alternate exterior angles are congruent, then the lines are parallel.

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.

If two lines are cut by a transversal such that the consecutive interior angles are supplementary then the lines are parallel.

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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