I have a geometry question. I understand the question and its possible answers, but the answer isn't clear enough that I understand what it is asking. Can someone please help me and look at the question?

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I have a geometry question. I understand the question and its possible answers, but the answer isn't clear enough that I understand what it is asking. Can someone please help me and look at the question?

Mathematics
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Angle 4 is congruent to angle 6. Choose the correct statement.
1 Attachment
The three choices are: a. r is sometimes parallel to t. b. r is always parallel to t. c. r is never parallel to t.
Please help. (My brother closed this question on accident.. :/

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Do you know the name given to a pair of angles like angles 4 and 6 with regard to parallel lines? For example, are they corresponding angles?
Same-side interior.
Correct.
I chose "sometimes" for this question, as I thought this was a very general question; not enough evidence was provided for me to fully understand the question. I'm not sure if what I chose was correct, though.
Could angles 4 and 6 both be equal to 40 degrees? That is, is it possible? All we know about them is that they are congruent.
I don't think so, there are no tick marks, so I can't be sure, but I assume that they both are 90 degrees.
And they are too close to being perpendicular to being 40 degrees.
It is not correct to assume that the angles have measure 90 each just because they look like right angles.
If we knew that the lines were parallel, then angles 4 and 6 would each be 90. But we do not know that the lines are parallel.
In order to find the answer, do we have to use proof (as in proving with reasons and statements), or just pick 1 of the 3 answers provided based on evidence?
For all we know, angles 4 and 6 could each be 40 degrees in which case the lines would not be parallel because same side interior angles of parallel lines are supplementary (sum to 180).
No need for a proof. If you think the answer is "sometimes," then show two values for 4 and 6 that make the lines parallel. Then, show 2 values for angles 4 and 6 that would not make the lines parallel.
Alright, thank you!
>And they are too close to being perpendicular to being 40 degrees. You can't judge angle size from the diagram.
Thank you for being patient with me as well.
If angles 4 and 6 are each 40 degrees, then they are congruent. But, they do not sum to 180, so that is a time when the lines would not be parallel.
The main reason why I assumed they were right angles were because they are same-side interior angles, and supplementary.
But, angles 4 and 6 could each be 90 degrees because that makes them congruent. 90 + 90 = 180. The same side interior angles are then supplementary. The two lines are parallel.
So, there is a case in which the lines are not parallel (each angle 40) and then there is a case in which the lines are parallel (each angle 90). The result is sometimes as you guessed.
>>The main reason why I assumed they were right angles were because they are same-side interior angles, and supplementary. You do not know that the two angles are supplementary unless you are given that the lines are parallel. You were not given that the lines are parallel. Looking at a geometry diagram and making conclusions about size is dangerous. An angle is right only if it is given to be right.
Okay?
Yes.
This also helped me with another one of my problems similar to this, so I now know what the correct answer is, using what we discussed. (These questions confuse me because they are not very specific about whether it is in general, or about the graph provided.) So, thank you so much for being patient and explaining things to me!
You are welcome. If you want to do so, post the next problem in a new thread and post what you got for the answer, and we can compare answers. Okay?
I think I understand the next few problems of my assignment, but thank you for offering to help.
Okay.

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