## anonymous one year ago Proportionality Theorem I have the first column of the proof I just need help with the second.

1. anonymous

2. anonymous

3. anonymous

@jim_thompson5910

4. anonymous

the first two are most likely incorrect

5. anonymous

Any ideas? :/

6. jim_thompson5910

why do you think the first two are incorrect?

7. anonymous

I am over all unsure about proofs. I am horrible when it comes to them

8. jim_thompson5910

see attached

9. anonymous

oh wow.

10. anonymous

guess I was right :p

11. jim_thompson5910

right in that the first two lines of the 2 column proof are incorrect? Or that they are correct?

12. anonymous

They are correct. :p

13. anonymous

2 down 4 more lines to figure out .-.

14. jim_thompson5910

why is angle ABC congruent to angle ADE ?

15. anonymous

I dont know. because they're congruent angles?

16. jim_thompson5910

That's circular reasoning and flawed. You cannot make a statement and then back up that statement with the same statement.

17. jim_thompson5910
18. anonymous

ugh. I hate proofs. Does it have to do with Bisectors?

19. jim_thompson5910

go ahead and look through the link I posted be sure to play with the interactive applet

20. anonymous

They're corresponding angles?

21. jim_thompson5910

very good

22. jim_thompson5910

|dw:1433203991985:dw|

23. jim_thompson5910

|dw:1433204002334:dw|

24. jim_thompson5910

what about the next line?

25. anonymous

one sec lemme fill in the third

26. anonymous

Alrighty. give me a second to look on that link

27. anonymous

this one confuses me.. possibly consecutive interior angles?

28. jim_thompson5910

why?

29. anonymous

theres angles in and outside.. kind of.

30. jim_thompson5910

|dw:1433204262730:dw|

31. jim_thompson5910

we are given that DE || BC |dw:1433204337699:dw|

32. jim_thompson5910

and as you pointed out \[\Large \sphericalangle ABC \cong \sphericalangle ADE\] because they are corresponding angles |dw:1433204439413:dw|

33. anonymous

Alright...

34. jim_thompson5910

The same applies for angle ACB and angle AED \[\Large \sphericalangle ACB \cong \sphericalangle AED\] because they are corresponding angles |dw:1433204518237:dw|

35. anonymous

soo corresponding angles again?

36. jim_thompson5910

correct

37. anonymous

Now the 5th line to me makes no sense its like a triangle then a segment

38. jim_thompson5910

oops typo

39. jim_thompson5910

let me fix

40. anonymous

i see what you mean. oops. aha

41. jim_thompson5910

42. anonymous

Intersecting Chords Theorem?

43. jim_thompson5910

nope

44. anonymous

so many theorems.

45. jim_thompson5910
46. jim_thompson5910

keep in mind that the 2 column proof builds up to what we want to aim for. Each step/line is necessary in getting to where we want to go

47. anonymous

AA?

48. jim_thompson5910

yep, Angle Angle |dw:1433205268084:dw|

49. jim_thompson5910

|dw:1433205298484:dw|

50. anonymous

Ohh.

51. jim_thompson5910

so we have a pair of congruent corresponding angles, therefore that's why \(\large \triangle ABC \sim \triangle DBA\) is true (because of the AA similarity theorem)

52. anonymous

I see what you mean.

53. anonymous

then what about the last one?

54. jim_thompson5910

any thoughts on it?

55. anonymous

I mean. I see how they relate. corresponding sides?

56. jim_thompson5910

how can we use line 5 to lead up to line 6 ?

57. anonymous

Honestly I have no idea.

58. jim_thompson5910

if you look through these theorems http://www.regentsprep.org/regents/math/geometry/gp11/LsimilarProof.htm which theorem deals with proportions?

59. anonymous

SSS!!!(:

60. jim_thompson5910

yes specifically the converse of the SSS similarity theorem

61. jim_thompson5910

the SSS similarity theorem if the sides are all in proportion (as shown in the fractions), then the triangles are similar

62. jim_thompson5910

converse of the SSS similarity theorem if the triangles are similar, then the sides form a proportion

63. jim_thompson5910

the converse is the "backwards" version of the original, so to speak

64. anonymous

I see. so does this look good?

65. jim_thompson5910

it's not just SSS theorem, it's the converse of that theorem

66. jim_thompson5910

everything else looks good though

67. anonymous

so write converse sss theorem?

68. jim_thompson5910

yeah or something like that so the teacher knows

69. anonymous

BTW this isn't a test or quiz or anything.. I see alot of students ask for answers on here.

70. jim_thompson5910

ok I hope that it's not. Those sorts of things should be taken individually without any help. If anything, they should be proctored.

71. anonymous

Anyways Thank you for the help!! It means the world!

72. jim_thompson5910

you're welcome