Because A and X are corresponding angles, the sides opposite them are corresponding. So $\displaystyle{\overline{{{B}{C}}}}\leftrightarrow{\overline{{{Y}{Z}}}}\usepackage{cmbright}\Huge\$ . Because B and Y are corresponding angles, the sides opposite them are corresponding. So $\displaystyle{\overline{{{A}{C}}}}\leftrightarrow{\overline{{{X}{Z}}}}.\usepackage{cmbright}\Huge\$ Because two pairs of corresponding angles have the same measures ( $\displaystyle{m}\angle{A}={m}\angle{X}\usepackage{cmbright}\Huge\$ and $\displaystyle{m}\angle{B}={m}\angle{Y}\usepackage{cmbright}\Huge\$ ), the third pair of corresponding angles must be congruent. So $\displaystyle\angle{C}\leftrightarrow\angle{Z}\usepackage{cmbright}\Huge\$ , and therefore $\displaystyle{\overline{{{A}{B}}}}\leftrightarrow{\overline{{{X}{Y}}}}\usepackage{cmbright}\Huge\$ .