Rotate △P'Q'R' about point X to get △P''Q''R'' where R''=X and coincide. Since translation and rotation preserve , R''Q''=RQ=XW, which means . Since translation and rotation also preserve , m∠Q''R''P''=m∠QRP=m∠WXV, and point V lies on . Similarly, point V lies on Q''P'' . Both are at the intersection of R''P'' and Q''P'' and the intersection of two rays is a unique point, so . Therefore, △PQR can be mapped onto △VWX by a sequence of rigid transformations, and △PQR≅△VWX.
