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Flexi Quads

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

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Three by One

There are many different methods to solve this geometrical problem - how many can you find?

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Flexi Quad Tan

As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.

Tetra Perp

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Why do this problem?
A well known result but nevertheless a good exercise in using vectors including the scalar product.

Key question
How do you write down what is given in the question in terms of vectors?