Square It
Play with this interactivity until you can draw tilted squares confidently.
You could fix one side of a square and then work out where the other corners need to go.
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Bendy Quad
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
Lawnmower
A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of grass exactly one foot wide and wishes to cut the entire lawn in parallel strips. What is the minimum number of strips the gardener must mow?
Long Short
What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?