1. The problem asks us to complete the statement about the congruence of triangles after a reflection across the y-axis. 2. Reflection across the y-axis is a type of rigid transformation. 3. A rigid transformation preserves the lengths of sides and the measures of all angles. 4. Therefore, the two triangles are congruent because the transformation is rigid and preserves side lengths and angle measures. 5. The completed statement is: "The two triangles **are** congruent because the transformation is a rigid transformation, which **preserves** the lengths of the sides and measures of all angles."