= Let A, B, C, X and A, B', C', X' be points in an Euclidean Plane so that the segments [AC],[XC], [BC] are congruent to the segments (A'C'], [X'C'], [B'C'] respectively (i.e. d(A,C) d(A', C'), d(X,C) = d(X', C'), d(B,C) = d(B', C')). Also assume that X lies between A, B and X' lies between A', B', and that the angles at X respectively X' are right angles, i.e. |ZAXC| = \ZBXC| = | ZA'X'C'| = |_'X'C'| = 90 . Prove that the triangles AABC and AA'B'C' are congruent. Can we drop the assumption that X lies between A, B and X' between A'B