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!!

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- May 1st 2011, 07:39 PMjzelltRegular Quadrilateral Proof
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 PMTheChaz
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 PMjzellt
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 PMTheChaz
- May 1st 2011, 08:10 PMjzellt
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 PMjzellt
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 PMbjhopper
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