According to the given information, quadrilateral rect is a rectangle. by the definition of a rectangle, all four angles measure 90°. segment er is parallel to segment ct and segment ec is parallel to segment rt by the converse of the same-side interior angles theorem. quadrilateral rect is then a parallelogram by definition of a parallelogram. now, construct diagonals et and cr. because rect is a parallelogram, opposite sides are congruent. therefore, one can say that segment er is congruent to segment ct. segment tr is congruent to itself by the reflexive property of equality. the side-angle-side (sas) theorem says and because corresponding parts of congruent triangles are congruent (cpctc), diagonals et and cr are congruent.