Using facts about the angles formed when parallel lines are cut by a transversal, what relationship can you establish between angle 5 and angle 1?
Responses
alternate interior angles
alternate interior angles - no response given
vertical angles
vertical angles - no response given
corresponding angles
corresponding angles - not selected, this is the correct answer
alternate exterior angles
please show work
To establish the relationship between angle 5 and angle 1, we need to know the angle relationships formed when parallel lines are cut by a transversal.
When parallel lines are cut by a transversal, the following angle relationships are formed:
1. Alternate interior angles: These angles are located on opposite sides of the transversal and inside the two parallel lines. They are congruent (have the same measure). In this case, angle 5 and angle 1 are not alternate interior angles because they are not located on opposite sides of the transversal.
2. Vertical angles: These angles are formed by the intersection of two lines and are opposite each other. They are always congruent. Since angle 5 and angle 1 are not opposite each other, they are not vertical angles.
3. Corresponding angles: These angles are in the same position relative to the transversal. They are congruent. In this case, angle 5 and angle 1 are corresponding angles because they are in the same position relative to the transversal.
4. Alternate exterior angles: These angles are located on opposite sides of the transversal and outside the two parallel lines. They are congruent. Angle 5 and angle 1 are not alternate exterior angles because they are not located on opposite sides of the transversal.
Therefore, the correct relationship established between angle 5 and angle 1 is that they are corresponding angles.