Question
Which diagram represents the hypothesis of the converse of corresponding angles theorem?
Parallel lines m and n are cut by a transversal. The angles at the top right of both intersections are congruent.
Parallel lines p and q are cut by a transversal. The angles at the top left of the intersection with the first line and the bottom right of the intersection with the second line are congruent.
Parallel lines x and y are cut by a transversal. The angles at the bottom left of the intersection with the first line and the top right of the intersection with the second line are congruent.
Parallel lines m and n are cut by a transversal. The angles at the top right of both intersections are congruent.
Parallel lines p and q are cut by a transversal. The angles at the top left of the intersection with the first line and the bottom right of the intersection with the second line are congruent.
Parallel lines x and y are cut by a transversal. The angles at the bottom left of the intersection with the first line and the top right of the intersection with the second line are congruent.
Answers
GPT-4o mini
The converse of the Corresponding Angles Theorem states that if two lines are cut by a transversal and the corresponding angles are congruent, then the two lines are parallel.
Given your descriptions of the diagrams, the correct choice that represents the hypothesis of the converse of the corresponding angles theorem would be:
**Parallel lines m and n are cut by a transversal. The angles at the top right of both intersections are congruent.**
This scenario shows that if the corresponding angles at the intersections are congruent, then it can be concluded that lines m and n are parallel.
The other two options involve angles that are not directly corresponding angles as per the definition, hence they do not represent the hypothesis of the converse of this theorem.
Given your descriptions of the diagrams, the correct choice that represents the hypothesis of the converse of the corresponding angles theorem would be:
**Parallel lines m and n are cut by a transversal. The angles at the top right of both intersections are congruent.**
This scenario shows that if the corresponding angles at the intersections are congruent, then it can be concluded that lines m and n are parallel.
The other two options involve angles that are not directly corresponding angles as per the definition, hence they do not represent the hypothesis of the converse of this theorem.