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Parallelogram and similar triangles

Source: Dutch NMO 2000

October 22, 2005
geometryparallelogramtrapezoidsimilar triangles

Problem Statement

Isosceles, similar triangles QPAQPA and SPBSPB are constructed (outwards) on the sides of parallelogram PQRSPQRS (where PQ=AQPQ = AQ and PS=BSPS = BS). Prove that triangles RABRAB, QPAQPA and SPBSPB are similar.
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