Using facts about the angles formed when parallel lines ar cut by a transversal what relationship can you
conclude?
When parallel lines are cut by a transversal, several relationships can be concluded based on the facts about the angles formed. Some of these relationships include:
1. Corresponding angles are congruent: Corresponding angles are the angles that are in the same position in relation to the transversal and the parallel lines. They are located on the same side of the transversal and in corresponding positions on each of the parallel lines. Corresponding angles are always congruent.
2. Alternate interior angles are congruent: Alternate interior angles are the angles that are on opposite sides of the transversal and inside the parallel lines. They are located on different parallel lines, but on the same side of the transversal. Alternate interior angles are always congruent.
3. Alternate exterior angles are congruent: Alternate exterior angles are the angles that are on opposite sides of the transversal and outside the parallel lines. They are located on different parallel lines, but on the same side of the transversal. Alternate exterior angles are always congruent.
4. Same-side interior angles are supplementary: Same-side interior angles are the angles that are on the same side of the transversal and inside the parallel lines. They are located on different parallel lines, but on the same side of the transversal. Same-side interior angles are always supplementary, meaning their measures add up to 180 degrees.
These relationships can be used to solve angle problems and prove various geometric theorems.