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Rati-o
Age 11 to 14
Challenge Level 
An additional challenge here is to show that the inscribed polygon
is a parallelogram. Invite students to make conjectures about the
shape of this quadrilateral and then to prove their
conjectures.
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Isosceles
Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.
Linkage
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?