6. QUADRILATERAL WITH FIXED SIDES

· You are given four sides j, k, l, m, in order.

a. For what relation of the sides j, k. l. m will there be a quadrilateral/ or not?

b. Make a quadrilateral with colored sticks and fasteners.

c. What question would you like to ask about the set of all quadrilaterals with given sides jklm? what conjectures can you come up with?

d. On Sketchpad, construct a quadrilateral with given sides jklm in order which can be manipulated to give the set of all such quadrilaterals. Make a conjecture/ask a question and then explore. Describe what is true and why.

e. If the quadrilateral is crossed, what is the locus of the points where the crossed sides intersect? Why? If this is hard, let the original quadrilateral have opposite sides equal.