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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.
Which of the following completes the proof? (6 points)
1) Alternate Interior Angles Theorem
2) Converse of the Alternate Interior Angles Theorem
3) Converse of the Same-Side Interior Angles Theorem
Side Interior Angles Theorem