anonymous
  • anonymous
Geoffrey wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • 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
  • anonymous
anonymous
  • anonymous
Can someone please check to see if its correct?

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anonymous
  • anonymous
@amilapsn
anonymous
  • anonymous
@IrishBoy123
amilapsn
  • amilapsn
You say side angle side theorem right?
anonymous
  • anonymous
Yes, but i think im wrong.
amilapsn
  • amilapsn
hm... So what's your final decision?
anonymous
  • anonymous
I think is that one but im not sure, i just need help to understand it
anonymous
  • anonymous
Like explaining to me
amilapsn
  • amilapsn
ok let's mark what's in Geofrey's proof in the diagram... Can you do it for me?|dw:1440103234043:dw|
anonymous
  • anonymous
It states that Segment ER is parallel to segment CT and segment EC is parallel to segment RT
amilapsn
  • amilapsn
just click on the right top corner pencil of the diagram I just posted... You can mark the data yourself..
amilapsn
  • amilapsn
It would be fun. Believe me!
anonymous
  • anonymous
|dw:1440114097646:dw|
anonymous
  • anonymous
Sorry for the mess i was trying to make it dark enouugh.
amilapsn
  • amilapsn
No problem :)
amilapsn
  • amilapsn
Geoffrey says that segment ER is congruent to segment CT. Can you mark that?
anonymous
  • anonymous
|dw:1440114349257:dw|
amilapsn
  • amilapsn
And segment TR is congruent for itself... I'll mark that for you... or would you like to mark it yourself?
anonymous
  • anonymous
I could do it if you want
anonymous
  • anonymous
|dw:1440114527163:dw|
amilapsn
  • amilapsn
So now we have this:|dw:1440103862809:dw|
amilapsn
  • 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
  • anonymous
Yes, i got that!
amilapsn
  • amilapsn
Now we have to show that ET=RC. So what are the congruent triangles we have to consider?
anonymous
  • anonymous
EC and RT? i really dont know.
amilapsn
  • amilapsn
EC and RT are line segments. Now our goal is to show that ET=RC right?
anonymous
  • anonymous
Yes!
amilapsn
  • amilapsn
|dw:1440104396426:dw|
amilapsn
  • amilapsn
Very well... To show that what are the triangles we've to consider? Have a guess ;)
anonymous
  • anonymous
We have to prove the congruence?
amilapsn
  • amilapsn
yep
anonymous
  • anonymous
I was so nervous answering that.
amilapsn
  • amilapsn
look at what we've marked so far... you've to just tell me congruent triangles.... !!!
anonymous
  • anonymous
Okay let me figure it out
anonymous
  • anonymous
ert and ctr?
amilapsn
  • amilapsn
Gotcha!
anonymous
  • anonymous
You're awesome!
anonymous
  • anonymous
Was my first answer correct?
amilapsn
  • amilapsn
Yep... :)
anonymous
  • anonymous
Thank you so much for your help!
amilapsn
  • amilapsn
Yw!
anonymous
  • anonymous
I got it right in my test! thanksss
amilapsn
  • amilapsn
|dw:1440105512532:dw|
amilapsn
  • amilapsn
Don't be frightened to do mistakes... :)

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