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lines after symmetry of plane wrt line k

Source: Polish MO Recond Round 1979 p4

September 9, 2024
geometrysymmetry3D geometrylines

Problem Statement

Let Sk S_k be the symmetry of the plane with respect to the line k k . Prove that equality holds for every lines a,b,c a, b, c contained in one plane SaSbScSaSbScSbScSaSbScSa=SbScSaSbScSaSaSbScSaSbSc S_aS_bS_cS_aS_bS_cS_bS_cS_aS_bS_cS_a = S_bS_cS_aS_bS_cS_aS_aS_bS_cS_aS_bS_c
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