Question

Margot wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.

Answer 1

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.

Answer 2

Which of the following completes the proof? (6 points)
triangle ECR is congruent to triangle ECT
triangle ECT is congruent to triangle CER
triangle ERT is congruent to triangle CTR
triangle ETR is congruent to triangle ECR