Attachment 20039

In the figure above, FD || AC and EF || CB. Prove that ∠C≅∠EFD and that ∠CEF≅∠FDC.

Can someone offer help?

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- Dec 9th 2010, 07:13 AMtysonrssproving angles?
Attachment 20039

In the figure above, FD || AC and EF || CB. Prove that ∠C≅∠EFD and that ∠CEF≅∠FDC.

Can someone offer help? - Dec 9th 2010, 07:27 AMBariMutation
I can't quite remember the name of the theorem, but I know it exists. Remember that the picture I attached holds true. That is essentially what is happening with both of your questions, only with parallel lines. Notice that EF is cutting through the parallel lines of FD and AC. Are you following?

- Dec 9th 2010, 07:36 AMtysonrss
Err...yeah, I notice what its cutting through...but how does it relate to the picture you attached?

- Dec 9th 2010, 07:40 AMBariMutation
I just flipped the reference point, but it's still true. What about now? The red lines are, as you can guess, just the lines extended.

- Dec 9th 2010, 07:43 AMtysonrss
Gotcha, I think I understand the picture...but how does it help me solve the problem?

- Dec 9th 2010, 07:48 AMBariMutation
∠C≅∠EFD is what I actually drew in there, and ∠CEF≅∠FDC is the same theorem, just with the opposing (smaller) angles. Essentially, you just have to state the theorem and draw in what I did (at least that's what I assume you have to do. I can't imagine you have to prove the theorems too).

- Dec 9th 2010, 07:53 AMtysonrss
Actually there is no drawing. I think what they mean by proving is by writing it out somehow. This is computer work, not a worksheet.

- Dec 9th 2010, 07:56 AMBariMutation
Hm... are you able to do a T proof? For instance,

STATEMENT............THEOREM/INFORMATION

x=y...........................given in the problem

x=x..............................substitution - Dec 9th 2010, 08:00 AMtysonrss
Actually im not really sure. Novelstars--the website where I do my work on is a bit iffy when explaining things. If it helps I think the theorm is triangle sum theorem.

- Dec 9th 2010, 08:06 AMBariMutation
Well, if you're just turning in a typed paper, then use the T proof I showed you. However, if you have to enter your answer in a dialog line and press "OK" or something, I'd just say the theorems you used... are you able to take a screen shot of what you're seeing on the site?

- Dec 9th 2010, 08:17 AMUnknown008
The ones you used are the alternate (or Z) angles and the opposite angles (Smile)

This should be easy now. You can proove $\displaystyle \angle C \equiv \angle EFD$ directly from what BariMutation told you.

And using the fact that CDFE is a rhombus (or using the parallel lines again), you will see that $\displaystyle \angle CEF\equiv\angle FDC.$