Question

Please help me UNDERSTAND this math question! I have a feeling about the correct answer so I've already narrowed it down!!

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 ________________. 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.

Answer 2

Which of the following completes the proof?
Alternate Interior Angles Theorem
Converse of the Alternate Interior Angle Theorem
Converse of the Same-Side Angles Theorem
Same-Side Interior Angles Theorem

I'm thinking it has to be ONE of the last TWO.

Answer 3

Same-Side Interior Angles Theorem would prove the angles are supplementary once you know the segments are parallel.. They've already proven the angles are supplementary by the definition of the rectangle, and you don't know the segments are parallel yet.

Converse of the Same-Side Angles Theorem does the opposite. You know the angles are supplementary and you want to prove the segments are parallel. This is the correct reason