. How can you prove that a constructed line is parallel to a given line? Assume that the transversal line is not perpendicular to the other lines. 1 Show that same side exterior angles are congruent. 2 Show that same side interior angles are congruent. 3 Show that the transversal intersects both lines. 4 Show that corresponding angles are congruent.
To prove that a constructed line is parallel to a given line, you can use the alternate interior angles theorem. The steps for this proof are as follows:
1. Draw a transversal line that intersects both the given line and the constructed line.
2. If you want to prove that the constructed line is parallel to the given line, you need to show that alternate interior angles are congruent.
3. Identify a pair of alternate interior angles that are formed by the given line and the transversal line.
4. Identify a pair of alternate interior angles that are formed by the constructed line and the transversal line.
5. Use the congruent alternate interior angles to conclude that the constructed line is parallel to the given line.
Remember that alternate interior angles are located on opposite sides of the transversal line and between the two lines being intersected.