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Congruent quadrilaterals

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September 1, 2010
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Problem Statement

The diagonals of a quadrilateral ABCDABCD are perpendicular: AC⊥BDAC\perp BD. Four squares, ABEF,BCGH,CDIJ,DAKLABEF,BCGH,CDIJ,DAKL, are erected externally on its sides. The intersection points of the pairs of straight lines CL,DF;DF,AH;AH,BJ;BJ,CLCL,DF; DF,AH; AH,BJ; BJ,CL are denoted by P1,Q1,R1,S1P_1,Q_1,R_1, S_1, respectively, and the intersection points of the pairs of straight lines AI,BK;BK,CE;AI,BK; BK,CE; CE,DG;DG,AI CE,DG; DG,AI are denoted by P2,Q2,R2,S2P_2,Q_2,R_2, S_2, respectively. Prove that P1Q1R1S1≅P2Q2R2S2.P_1Q_1R_1S_1 \cong P_2Q_2R_2S_2.
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