• May 1st 2011, 07:39 PM
jzellt
Suppose that Quadrilateral ABCD has the property that (i) AD || BC and (ii) C and
D are on the same side of AB. Then Quadrilateral ABCD is regular.

This seems rather obvious, but I must have a proof of the above. Can someone show please. Thanks!!
• May 1st 2011, 07:42 PM
TheChaz
Quote:

Originally Posted by jzellt
Suppose that Quadrilateral ABCD has the property that (i) AD || BC and (ii) C and
D are on the same side of AB. Then Quadrilateral ABCD is regular.

This seems rather obvious, but I must have a proof of the above. Can someone show please. Thanks!!

This seems rather obviously false to me... unless "on the same side" is more specific than I realize.

Actually, would you care to elaborate on the meaning of "on the same side"? If we end up with a square based on this phrase, I sure would like to know its meaning...
• May 1st 2011, 07:55 PM
jzellt
Take the line AB. Then, C and D must be on the same side of the line... I'm sure where the confusion is here. Maybe try drawing it out... Thanks
• May 1st 2011, 08:01 PM
TheChaz
Quote:

Originally Posted by jzellt
Take the line AB. Then, C and D must be on the same side of the line... I'm sure where the confusion is here. Maybe try drawing it out... Thanks

I can draw a million such quadrilaterals that ARE NOT regular!

Take A, B, C, D to be:
(0, 0), (0, 1), (1, 1), and (2, 0) for example.

Like you, I am not sure where the confusion is here, but I have a good guess...
• May 1st 2011, 08:10 PM
jzellt
You're right... Thanks. This is a propostion right out of my professors lecture notes and I was asked to prove it. I guess he made a mistake... Thanks again
• May 1st 2011, 08:15 PM
jzellt
In my professor lecture notes, he states:
The following says that trapezoids (defined using the American convention, as opposed to
the British convention) are regular.
Then, the proposition is stated. So I guess I still need a proof the proposition posted in my original post...
• May 2nd 2011, 02:56 PM
bjhopper
Hello jzellt,
To define a regular trapezoid or a parallelogram something more than two parallel lines is required. For example the two parallel line segments are equal . you must be leaving something out

bjh