hhopke
  • hhopke
Prove that QR || US
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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hhopke
  • hhopke
mathstudent55
  • mathstudent55
What do you need to show to prove lines are parallel?
hhopke
  • hhopke
?

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hhopke
  • hhopke
That's what I have so far
mathstudent55
  • mathstudent55
This is what I mean by the question above. Here are lines m and n, and transversal t. |dw:1434568617945:dw|
hhopke
  • hhopke
But the picture doesn't look like that.
mathstudent55
  • 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
  • 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
  • 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
  • mathstudent55
Let's look at your figure, and reason out the steps in this proof.
mathstudent55
  • mathstudent55
|dw:1434569034493:dw|
mathstudent55
  • 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
  • hhopke
Yes.
mathstudent55
  • mathstudent55
Correct bec angles 2 and 6 are corresponding angles, and if they are congruent, the lines are parallel.
hhopke
  • 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
  • mathstudent55
I marked the parallel lines and the given congruent angles. |dw:1434569202980:dw|
mathstudent55
  • mathstudent55
We know angles 1 and 6 are congruent. We need to show that angles 2 and 6 are congruent.
hhopke
  • 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
  • mathstudent55
Exactly. That is it.
hhopke
  • hhopke
then 6 and 4 are congruent (vertical angles), so 4 is congruent to 1 and 2 (transitive property)
hhopke
  • hhopke
is that useful?
mathstudent55
  • mathstudent55
No. There is no need for 6 and 4
hhopke
  • hhopke
okay.
hhopke
  • hhopke
Now what?
mathstudent55
  • 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
  • mathstudent55
This is simpler proof than you originally thought.
hhopke
  • hhopke
we can prove that they're parallel with 2 and 6?
mathstudent55
  • mathstudent55
I'll go through your steps and we'll see what needs to be there.
hhopke
  • hhopke
Okay.
mathstudent55
  • 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
  • mathstudent55
I'd keep statement 1, drop statements 2, 3. Keep statement 4.
mathstudent55
  • mathstudent55
Drop statement 5.
mathstudent55
  • mathstudent55
keep statement 6 and 7
hhopke
  • hhopke
then drop 8 and add in the part about corresponding angles?
mathstudent55
  • mathstudent55
drop 8 and 9. where 8 was, state that the lines are parallel bec of what I wrote above with corresp angles.
hhopke
  • hhopke
Okay. Thank you so much!
mathstudent55
  • mathstudent55
You're welcome.

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