Prove that QR || US

Question

Prove that QR || US

hhopke · Answer

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mathstudent55 · Answer

What do you need to show to prove lines are parallel?

hhopke · Answer

?

hhopke · Answer

That's what I have so far

mathstudent55 · Answer

This is what I mean by the question above.
Here are lines m and n, and transversal t.
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hhopke · Answer

But the picture doesn't look like that.

mathstudent55 · Answer

Can you name a pair of angles in the figure below, that if you know they are congruent, then the lines m and n must be parallel?
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hhopke · Answer

There are a bunch (alt. ext, alt. int, corresponding, etc.) but I need to prove it with the given picture.|dw:1434568849868:dw|

mathstudent55 · Answer

Ok. Great answer.
I realize you are answering a different question with a different figure, but I needed to see if you knew how to prove lines parallel. Now I see that you do know.

mathstudent55 · Answer

Let's look at your figure, and reason out the steps in this proof.

mathstudent55 · Answer

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mathstudent55 · Answer

You need to prove lines QR and US parallel.
If you could show that angles 2 and 6 are congruent, would that help?

hhopke · Answer

Yes.

mathstudent55 · Answer

Correct bec angles 2 and 6 are corresponding angles, and if they are congruent, the lines are parallel.

hhopke · Answer

1 and 2 are alternate interior angles, so they are congruent (the lines are parallel) and 1 and 6 are congruent (given) so by transitive property 2 is congruent to 6 (that's how I did it)

mathstudent55 · Answer

I marked the parallel lines and the given congruent angles.
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