proving angles?

• Dec 9th 2010, 07:13 AM
proving 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 AM
BariMutation
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 AM
Err...yeah, I notice what its cutting through...but how does it relate to the picture you attached?
• Dec 9th 2010, 07:40 AM
BariMutation
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 AM
Gotcha, I think I understand the picture...but how does it help me solve the problem?
• Dec 9th 2010, 07:48 AM
BariMutation
∠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 AM
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 AM
BariMutation
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 AM
This should be easy now. You can proove $\angle C \equiv \angle EFD$ 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 $\angle CEF\equiv\angle FDC.$