Prove that QR || US

- hhopke

Prove that QR || US

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- hhopke

##### 1 Attachment

- mathstudent55

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

- hhopke

?

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- hhopke

That's what I have so far

##### 1 Attachment

- mathstudent55

This is what I mean by the question above.
Here are lines m and n, and transversal t.
|dw:1434568617945:dw|

- hhopke

But the picture doesn't look like that.

- mathstudent55

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?
|dw:1434568719599:dw|

- hhopke

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

- mathstudent55

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

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

- mathstudent55

|dw:1434569034493:dw|

- mathstudent55

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

- hhopke

Yes.

- mathstudent55

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

- hhopke

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

I marked the parallel lines and the given congruent angles.
|dw:1434569202980:dw|

- mathstudent55

We know angles 1 and 6 are congruent.
We need to show that angles 2 and 6 are congruent.

- hhopke

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

- mathstudent55

Exactly. That is it.

- hhopke

then 6 and 4 are congruent (vertical angles), so 4 is congruent to 1 and 2 (transitive property)

- hhopke

is that useful?

- mathstudent55

No. There is no need for 6 and 4

- hhopke

okay.

- hhopke

Now what?

- mathstudent55

Since you can prove the lines parallel with corresponding congruent angles 2 and 6, there is no need to take the extra steps of showing that angles 4 and 6 are congruent by vertical angles and then the lines are parallel by angles 2 and 4 being congruen alt int angles.

- mathstudent55

This is simpler proof than you originally thought.

- hhopke

we can prove that they're parallel with 2 and 6?

- mathstudent55

I'll go through your steps and we'll see what needs to be there.

- hhopke

Okay.

- mathstudent55

yes. 2 and 6 are corresponding angles. if you show that when two lines are cut by a transversal, corresp angles are congruent, then the lines are parallel.

- mathstudent55

I'd keep statement 1, drop statements 2, 3.
Keep statement 4.

- mathstudent55

Drop statement 5.

- mathstudent55

keep statement 6 and 7

- hhopke

then drop 8 and add in the part about corresponding angles?

- mathstudent55

drop 8 and 9.
where 8 was, state that the lines are parallel bec of what I wrote above with corresp angles.

- hhopke

Okay. Thank you so much!

- mathstudent55

You're welcome.

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