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Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC

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Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC  [#permalink]

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New post 17 Oct 2017, 23:48
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

42% (00:37) correct 58% (01:07) wrong based on 100 sessions

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Re: Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC  [#permalink]

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New post 18 Oct 2017, 02:57
(1) AED is similar to ABC, hence angle ADE= angle ABC which means that DE is parallel to BC
(2) From here we cannot deduce whether AE=EC, so Insufficient

Answer A
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Re: Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC  [#permalink]

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New post 18 Oct 2017, 03:16
1
a line parallel to one side of triangle divides the other two sides in equal proportion
hence a is sufficient
considering b
given CE=BD
but the bottom or base angles of triangle might be diff hence the lengths of sides CE and BD cant be confirmed
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Re: Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC  [#permalink]

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New post 23 Oct 2017, 18:30
E, I screwed this one up. Not a silly mistake, just a knowledge gap.

The missing link for me was to see that the angles of the smaller triangle were similar to the larger triangle.
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I'd love to hear any feedback or ways to improve my problem solving. I make a lot of silly mistakes. If you've had luck improving on stupid mistakes, I'd love to hear how you did it.

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Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC  [#permalink]

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New post 24 Oct 2017, 14:30
By Applying Midpoint Theorem, we can determine with the help of Statement 1 alone that DE is parallel to BC.

Statement 2 is Insufficient to provide proof of triangle similarity.

Hence, Ans A

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Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC  [#permalink]

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New post 24 Oct 2017, 20:19
1
A

From (1) AED is similar to ABC => angle ADE= angle ABC => DE is parallel to BC=> suff
From (2) There will be insufficient condition to ensure AED is similar to ABC => insuff
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Re: Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC  [#permalink]

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New post 02 Nov 2017, 10:51
Bunuel

how to prove that two lines are parallel? what should i look for ? interior angles to be supplementary?
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Re: Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC  [#permalink]

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New post 02 Nov 2017, 22:58
Psk13 wrote:
Bunuel

how to prove that two lines are parallel? what should i look for ? interior angles to be supplementary?


From (1) DE turns out to be a Midsegment of a Triangle (A line segment joining the midpoints of two sides of a triangle).

The midsegment is always parallel to the third side of the triangle.
• The midsegment is always half the length of the third side.
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Re: Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC &nbs [#permalink] 02 Nov 2017, 22:58
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