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What do you need to show to prove lines are parallel?
This is what I mean by the question above. Here are lines m and n, and transversal t. |dw:1434568617945:dw|
But the picture doesn't look like that.
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|
There are a bunch (alt. ext, alt. int, corresponding, etc.) but I need to prove it with the given picture.|dw:1434568849868:dw|
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.
Let's look at your figure, and reason out the steps in this proof.
You need to prove lines QR and US parallel. If you could show that angles 2 and 6 are congruent, would that help?
Correct bec angles 2 and 6 are corresponding angles, and if they are congruent, the lines are parallel.
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)
I marked the parallel lines and the given congruent angles. |dw:1434569202980:dw|
We know angles 1 and 6 are congruent. We need to show that angles 2 and 6 are congruent.
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
Exactly. That is it.
then 6 and 4 are congruent (vertical angles), so 4 is congruent to 1 and 2 (transitive property)
is that useful?
No. There is no need for 6 and 4
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.
This is simpler proof than you originally thought.
we can prove that they're parallel with 2 and 6?
I'll go through your steps and we'll see what needs to be there.
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.
I'd keep statement 1, drop statements 2, 3. Keep statement 4.
Drop statement 5.
keep statement 6 and 7
then drop 8 and add in the part about corresponding angles?
drop 8 and 9. where 8 was, state that the lines are parallel bec of what I wrote above with corresp angles.
Okay. Thank you so much!