Question

Geoffrey 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 _______________ 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

Can someone please check to see if its correct?

Answer 3

@amilapsn

Answer 4

@IrishBoy123

Answer 5

You say side angle side theorem right?

Answer 6

Yes, but i think im wrong.

Answer 7

hm... So what's your final decision?

Answer 8

I think is that one but im not sure, i just need help to understand it

Answer 9

Like explaining to me

Answer 10

ok let's mark what's in Geofrey's proof in the diagram... Can you do it for me?

Answer 11

It states that Segment ER is parallel to segment CT and segment EC is parallel to segment RT

Answer 12

just click on the right top corner pencil of the diagram I just posted... You can mark the data yourself..

Answer 13

It would be fun. Believe me!