## anonymous one year ago Geoffrey wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.

1. 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.

2. anonymous

3. anonymous

Can someone please check to see if its correct?

4. anonymous

@amilapsn

5. anonymous

@IrishBoy123

6. amilapsn

You say side angle side theorem right?

7. anonymous

Yes, but i think im wrong.

8. amilapsn

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

9. anonymous

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

10. anonymous

Like explaining to me

11. amilapsn

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

12. anonymous

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

13. amilapsn

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

14. amilapsn

It would be fun. Believe me!

15. anonymous

|dw:1440114097646:dw|

16. anonymous

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

17. amilapsn

No problem :)

18. amilapsn

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

19. anonymous

|dw:1440114349257:dw|

20. amilapsn

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

21. anonymous

I could do it if you want

22. anonymous

|dw:1440114527163:dw|

23. amilapsn

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

24. amilapsn

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

25. anonymous

Yes, i got that!

26. amilapsn

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

27. anonymous

EC and RT? i really dont know.

28. amilapsn

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

29. anonymous

Yes!

30. amilapsn

|dw:1440104396426:dw|

31. amilapsn

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

32. anonymous

We have to prove the congruence?

33. amilapsn

yep

34. anonymous

I was so nervous answering that.

35. amilapsn

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

36. anonymous

Okay let me figure it out

37. anonymous

ert and ctr?

38. amilapsn

Gotcha!

39. anonymous

You're awesome!

40. anonymous

41. amilapsn

Yep... :)

42. anonymous

Thank you so much for your help!

43. amilapsn

Yw!

44. anonymous

I got it right in my test! thanksss

45. amilapsn

|dw:1440105512532:dw|

46. amilapsn

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