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 please.

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.

kcreadergames kcreadergames · Answer 2 · 2021-03-17T15:59:19+01:00

Answer:

C. a || b, COnverse of the Alternate Interior Angles theorem

Step-by-step explanation:

TD;LR - ∠7 and ∠9 are on the interior sides of the lines a and b = converse Alternate Interior angles theorem

oIf you were to look at it using the lines c and d, like I did when I first saw this, it gets confusing and you can come to the conclusion it can't be exterior or interior because one is interior and the other exterior, so in order for this to make sense you have to look at it using a and b as the lines and c and d as the transitive lines. Knowing transitive property and how transitive lines work we come to the conclusion that ∠7 and ∠9 are interior angles for lines a and b letting us know it has to do with the Alternate interior angles theorem. This allows us to cross Options A and B off the list giving you a 50/50 chance of getting it right if you were to guess, but since we know that the angles are interior we can conclude that we did have enough information to figure it out, therefore C is the right answer and D is incorrect