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Tetra Inequalities
Age 16 to 18
Challenge Level 
Why use this problem?
This problem uses proof by contradiction to prove that a statement is true. Students will be required to think about inequalities (which they can often find difficult), and will need to construct a clear logical argument.
Key Questions
- Can you write down the lengths of some possible triangles?
- Can you write down three lengths which cannot be the lengths of the triangle?
- If a triangle has lengths $a, b$ and $c$, what inequality must the lengths satisfy?
- If $p>q$ and $r>s$, what can you say about $p+r$?
The problem Tetrahedron Tester could be used as an introduction to the triangle inequality.
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