The answer is segment EC is parallel to segment RT.
Spencer wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.
Quadrilateral R E C T is shown with right angles at each of the four corners. Segments E R and C T have single hash marks indicating they are congruent while segments E C and R T have two arrows indicating they are parallel. Segments E T and C R are drawn.
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 ________________. 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 triangle ERT is congruent to triangle CTR. And because corresponding parts of congruent triangles are congruent (CPCTC), diagonals ET and CR are congruent.
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