Here is a Quadrilateral challenge.
Step 1. Draw any irregular quadrilateral. Don't make a trapezoid or parallelogram or kite. That's too obvious. Draw something like this:
Step 2. Find all the midpoints of each side of the quadrilateral.
Step 3. Connect the midpoints to form a new quadrilateral.
Step 4. What kind of quadrilateral is form? Justify your feelings.
Step 5. Try it again, varying your shape a bit. Repeat the steps? Did you get the same (or a similar) result? Why do you think that happened?
Hint: Here's what my image looks like: