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

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Math Expert
Joined: 02 Sep 2009
Posts: 51185
Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC  [#permalink]

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17 Oct 2017, 22:48
00:00

Difficulty:

75% (hard)

Question Stats:

38% (01:12) correct 63% (01:38) wrong based on 102 sessions

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If DB = AD, is DE parallel to BC ?

(1) AE = EC
(2) DB = EC

Attachment:

2017-10-18_1046.png [ 3.9 KiB | Viewed 2260 times ]

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

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18 Oct 2017, 01:57
(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

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

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18 Oct 2017, 02:16
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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23 Oct 2017, 17:30
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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Is DE parallel to BC ? DB = AD. (1) AE = EC (2) DB = EC  [#permalink]

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24 Oct 2017, 13:30
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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24 Oct 2017, 19:19
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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02 Nov 2017, 09:51
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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02 Nov 2017, 21:58
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, 21:58
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