Question

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

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 _______________ says triangle ERT is congruent to triangle CTR.
And because corresponding parts of congruent triangles are congruent (CPCTC), diagonals ET and CR are congruent.

Answer 1

The correct answer is (SAS) I was just working on this and got it correct.

Answer 2

the answer
The triangle congruence says triangle ERT is congruent to triangle CTR.