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##### Age 14 to 16Challenge Level

You may find it useful to print off some dotty paper for this task.

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.

What do you notice about the new quadrilaterals formed by joining the midpoints?
Does this always happen?

Can you find a counter-example?
Can you make a conjecture?
You may wish to use the GeoGebra interactivity to explore.