The points P, Q, R and S are the midpoints of the edges of a convex
quadrilateral. What do you notice about the quadrilateral PQRS as
the convex quadrilateral changes?
The points P, Q, R and S are the midpoints of the edges of a
non-convex quadrilateral.What do you notice about the quadrilateral
PQRS and its area?
Can you find the area of a parallelogram defined by two vectors?
Four rods, two of length a and two of length b, are linked to form
a kite. The linkage is moveable so that the angles change. What is
the maximum area of the kite?
Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.
ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.
We have four rods of equal lengths hinged at their endpoints to
form a rhombus ABCD. Keeping AB fixed we allow CD to take all
possible positions in the plane. What is the locus (or path) of the
point. . . .