Converse of the Parallel Lines Theorem
The Corresponding Angles Theorem states that if parallel lines are cut by a transversal, then their corresponding angles are congruent. Use this GeoGebra construction to determine if the converse of that theorem is true. If two lines are cut by a transversal so that the corresponding angles are congruent, are the lines always parallel? Is there any way to construct the line through the transversal with congruent corresponding angles so that they are not parallel?
Check the angle measure box to view the measure of one of the angles formed by the intersecting lines. In order to copy the angle along the transversal, check the Copy Angle box. Then you will be able to view the line through the congruent angle by checking another box. Are the lines parallel? Is there any way to make the lines intersect, while keeping the angles congruent?