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

- anonymous

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- anonymous

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.

- anonymous

##### 2 Attachments

- anonymous

Can someone please check to see if its correct?

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## More answers

- anonymous

@amilapsn

- anonymous

@IrishBoy123

- amilapsn

You say side angle side theorem right?

- anonymous

Yes, but i think im wrong.

- amilapsn

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

- anonymous

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

- anonymous

Like explaining to me

- amilapsn

ok let's mark what's in Geofrey's proof in the diagram... Can you do it for me?|dw:1440103234043:dw|

- anonymous

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

- amilapsn

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

- amilapsn

It would be fun. Believe me!

- anonymous

|dw:1440114097646:dw|

- anonymous

Sorry for the mess i was trying to make it dark enouugh.

- amilapsn

No problem :)

- amilapsn

Geoffrey says that segment ER is congruent to segment CT. Can you mark that?

- anonymous

|dw:1440114349257:dw|

- amilapsn

And segment TR is congruent for itself... I'll mark that for you... or would you like to mark it yourself?

- anonymous

I could do it if you want

- anonymous

|dw:1440114527163:dw|

- amilapsn

So now we have this:|dw:1440103862809:dw|

- amilapsn

I've shown that ER=CT by putting one line over them and RT=RT by putting two lines... Did you get that?

- anonymous

Yes, i got that!

- amilapsn

Now we have to show that ET=RC. So what are the congruent triangles we have to consider?

- anonymous

EC and RT? i really dont know.

- amilapsn

EC and RT are line segments. Now our goal is to show that ET=RC right?

- anonymous

Yes!

- amilapsn

|dw:1440104396426:dw|

- amilapsn

Very well... To show that what are the triangles we've to consider? Have a guess ;)

- anonymous

We have to prove the congruence?

- amilapsn

yep

- anonymous

I was so nervous answering that.

- amilapsn

look at what we've marked so far... you've to just tell me congruent triangles.... !!!

- anonymous

Okay let me figure it out

- anonymous

ert and ctr?

- amilapsn

Gotcha!

- anonymous

You're awesome!

- anonymous

Was my first answer correct?

- amilapsn

Yep... :)

- anonymous

Thank you so much for your help!

- amilapsn

Yw!

- anonymous

I got it right in my test! thanksss

- amilapsn

|dw:1440105512532:dw|

- amilapsn

Don't be frightened to do mistakes... :)

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