Parallel Lines and Planes

[Bordersalsaverde]

Okay. Here's my problem. At the beginning of the lesson, it says that parallel lines are lines in the same plane that never intersect. From my point of view, "D" never intersects, but neither does "a". Am I missing the whole point of the lesson? Can anyone help me understand this better?
If m∠T = m∠PUQ, which lines are parallel?

a.) None of the lines are parallel.
b.) RT || UQ
c.) PU || RS
d.) US || PR

 

[DrPhil]

View attachment 2702
Okay. Here's my problem. At the beginning of the lesson, it says that parallel lines are lines in the same plane that never intersect. From my point of view, "D" never intersects, but neither does "a". Am I missing the whole point of the lesson? Can anyone help me understand this better?
If m∠T = m∠PUQ, which lines are parallel?

a.) None of the lines are parallel.
b.) RT || UQ
c.) PU || RS
d.) US || PR

Lets look at the two angles that have the same measure .. i.e., are congruent. Those two angles are PUQ and PTR. Suppose you are traveling from P to T but you turn off at U. Or another time you go all the way to T and turn of by exactly the same angle. Because of the equal angles, the lines UQ and TR are parallel.

Perhaps you have already proved a theorem in class that covers this situation?

[It is possible that another pair of lines is parallel, but you have no way to prove it.]

 

[Bordersalsaverde]

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Thank you. I'm actually doing this as an online class. I've failed Geometry twice, and it's just not getting stuck in my head for some reason.
The lessons they've put up online for me are written in a way extremely hard to understand. Your way of teaching actually helped. Putting it in terms of traveling, I mean. Thanks again!

 

[tmoria]

... From my point of view, "D" never intersects, but neither does "a".

Did you mean (b) and (d) ?

Yes, they both certainly 'look' correct. However, from the information given you can only state that (b) is correct.

 

[Bordersalsaverde]

Yes, I meant "b" and "d." Sorry.