Pythagoras' theorem
These problems use the Pythagoras theorem and its consequences (perpendicularity criteria, projections, and equal‑tangent loci) to prove algebraic relations and describe geometric sets.
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These problems use the Pythagoras theorem and its consequences (perpendicularity criteria, projections, and equal‑tangent loci) to prove algebraic relations and describe geometric sets.
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These problems use the Pythagoras theorem and its consequences (perpendicularity criteria, projections, and equal‑tangent loci) to prove algebraic relations and describe geometric sets.
Before diving into geometric problems, it is useful to recall how the Pythagoras theorem and related algebraic identities appear from simple geometric dissections. Many classical proofs of Pythagoras are based on rearranging squares and triangles, or on counting areas. The following problems illustrate this connection.