Draw any convex quadrilateral and find the midpoints of the four edges. Join the midpoints to form a new quadrilateral.
Try it a few times starting with different convex quadrilaterals. You may like to use the GeoGebra interactivity to explore.
What do you notice about the new quadrilaterals formed by joining the midpoints?
Can you make a conjecture?
Can you prove it?
Is the area of PQRS always the same fraction of the area of ABCD? Can you explain why?
What if ABCD is a concave quadrilateral?