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!!

2. 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...

3. 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

4. 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...

5. 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

6. 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...

7. 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