This question is pretty confusing. given ∠7 ≅ ∠9, which lines, if any, must be parallel based on the given information? justify your conclusion. a. a║b, converse of the alternate exterior angles theorem b. c║d, converse of the same-side interior angles theorem c. a║b, converse of the alternate interior angles theorem d. not enough information to make a conclusion i'd like an explanation as well .

Looking at the provided diagram â 7 and â 9 are alternate interior angles. The reason for this is that those two angles are on alternate sides of the transversal line c. And they're interior angles because they're on the inside of the two lines a and b that are being transversed. And because those two angles are equal to each other, that means that lines a and b are parallel to each other. With this in mind, let's look at the available options. A. aâ•‘b, Converse of the Alternate Exterior Angles Theorem * Yes, a and b are parallel. But â 7 and â 9 are alternate interior angles, not alternate exterior angles. So this is a bad choice. B. câ•‘d, Converse of the Same-Side Interior Angles Theorem * We don't have any basis to see if c and d are parallel to each other or not. So this too is a bad choice. C. aâ•‘b, Converse of the Alternate Interior Angles Theorem * a and b are parallel to each other, so the first part is good. And â 7 and â 9 are alternate interior angles, so the second part matches as well. This is the correct choice. D. not enough information to make a conclusion * This is just abandoning the problem and since we've already picked C, it's a bad choice.

For the first question the answer is a, for the second c, for the third d, for the 4th b, for the 5th a