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Which are the parallel lines? alt text

I prove that $a$ and $b$ are parallel but can't prove that $c$ and $d$ are parallel. The angles, which are $135^o$ and $45^o$ are alternate angles.They aren't equal , so $c$ isn't parallel to $d$ but the answer is that $c$ is parallel to $d$. Am I right that they aren't?

Edit: They are a little inclined like these:

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To put it simply, yes. If the answer is that they are parallel, I suspect there is more to this than your description allows. –  Brandon Carter Nov 14 '10 at 9:09
Moreover, if the angles are how you say they are, then $C$ and $D$ are perpendicular... –  Brandon Carter Nov 14 '10 at 9:10
Have you tried making an accurate drawing? –  Guess who it is. Nov 14 '10 at 9:14
@Carter , they aren't perpendicular.My drawing is wrong. –  lam3r4370 Nov 14 '10 at 9:15
Note that $135+45=180$. –  Yuval Filmus Nov 14 '10 at 10:03

2 Answers 2

This is a problem with extra information. Part of solving problems is knowing what to ignore! You are thinking about 4 lines, but to show two lines are parallel, you only really need 3.

So, you don't need to use all of the information given to solve this problem. In fact, you can ignore line d and just focus on how line c interacts with the lines you want to prove are parallel.

Next look at the theorem about parallel lines and their transverse again.

Then, you should have your proof.

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Use corresponding angles to see if the lines are parallel. Note if the alternate interior angles are congruent. This will prove if any of these two pairs might fall under the category of Euclidean parallel lines.

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