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In the triangle above, DC is parallel to AB. What is the len

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danzig
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In the triangle above, DC is parallel to AB. What is the len [#permalink] New post   Updated on: 05 Mar 2023, 09:46
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In the triangle above, DC is parallel to AB. What is the length of DC?

(1) AB = 14
(2) EC = CB

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Attachment:
Triangle.jpg
Triangle.jpg [ 13.9 KiB | Viewed 5018 times ]

Please, confirm whether my solution is correct. If we consider both statements, we can notice that triangles AEB and DEC are the "same" triangle, except for the size. In other words, both have the same angles. Therefore, the relationship between any of two of their sides must be the same. Then,

\(\frac{14}{EB} = \frac{DC}{EC}\)

But we know that EC = 0.5*EB

Then: DC = 7

My answer is the OA.

Is it valid what I have done? I remember that I learned this in high school :s.
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C

Originally posted by danzig on 11 Jul 2013, 11:49.
Last edited by Bunuel on 05 Mar 2023, 09:46, edited 2 times in total.
Edited the question.
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In the triangle above, DC is parallel to AB. What is the len [#permalink] New post   11 Jul 2013, 12:21
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danzig wrote:


In the triangle above, DC is parallel to AB. What is the length of DC?

(1) AB = 14
(2) EC = CB

Please, confirm whether my solution is correct. If we consider both statements, we can notice that triangles AEB and DEC are the "same" triangle, except for the size. In other words, both have the same angles. Therefore, the relationship between any of two of their sides must be the same. Then,

\(\frac{14}{EB} = \frac{DC}{EC}\)

But we know that EC = 0.5*EB

Then: DC = 7

My answer is the OA.

Is it valid what I have done? I remember that I learned this in high school :s.


Yes, your solution is correct.

Else you can notice that DC is the midsegment (a line segment joining the midpoints of two sides of a triangle). The midsegment is always half the length of the third side, thus DC=AB/2=7.

Answer: C.

Similar questions to practice:
https://gmatclub.com/forum/if-be-cd-and ... 27060.html
https://gmatclub.com/forum/if-b-is-the- ... 27104.html
https://gmatclub.com/forum/ds-geometry- ... 28687.html
https://gmatclub.com/forum/in-triangle- ... 82671.html
https://gmatclub.com/forum/abcd-is-quad ... 31462.html

Hope it's clear.
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Urvasi
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Re: In the triangle above, DC is parallel to AB. What is the len [#permalink] New post   05 Mar 2023, 08:36
Bunuel wrote:
danzig wrote:
Attachment:
Triangle.jpg
In the triangle above, DC is parallel to AB. What is the length of DC?

(1) AB = 14
(2) EC = CB

Please, confirm whether my solution is correct. If we consider both statements, we can notice that triangles AEB and DEC are the "same" triangle, except for the size. In other words, both have the same angles. Therefore, the relationship between any of two of their sides must be the same. Then,

\(\frac{14}{EB} = \frac{DC}{EC}\)

But we know that EC = 0.5*EB

Then: DC = 7

My answer is the OA.

Is it valid what I have done? I remember that I learned this in high school :s.


Yes, your solution is correct.

Else you can notice that DC is the midsegment (a line segment joining the midpoints of two sides of a triangle). The midsegment is always half the length of the third side, thus DC=AB/2=7.

Answer: C.

Similar questions to practice:
https://gmatclub.com/forum/if-be-cd-and ... 27060.html
https://gmatclub.com/forum/if-b-is-the- ... 27104.html
https://gmatclub.com/forum/ds-geometry- ... 28687.html
https://gmatclub.com/forum/in-triangle- ... 82671.html
https://gmatclub.com/forum/abcd-is-quad ... 31462.html

Hope it's clear.


Is it ok to infer that DC is the mid segment? DC can be parallel without being mid segment; In that case the answer will change
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Bunuel
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In the triangle above, DC is parallel to AB. What is the len [#permalink] New post   05 Mar 2023, 09:51
Expert Reply
Urvasi wrote:
Bunuel wrote:
danzig wrote:


In the triangle above, DC is parallel to AB. What is the length of DC?

(1) AB = 14
(2) EC = CB

Please, confirm whether my solution is correct. If we consider both statements, we can notice that triangles AEB and DEC are the "same" triangle, except for the size. In other words, both have the same angles. Therefore, the relationship between any of two of their sides must be the same. Then,

\(\frac{14}{EB} = \frac{DC}{EC}\)

But we know that EC = 0.5*EB

Then: DC = 7

My answer is the OA.

Is it valid what I have done? I remember that I learned this in high school :s.


Yes, your solution is correct.

Else you can notice that DC is the midsegment (a line segment joining the midpoints of two sides of a triangle). The midsegment is always half the length of the third side, thus DC=AB/2=7.

Answer: C.

Similar questions to practice:
https://gmatclub.com/forum/if-be-cd-and ... 27060.html
https://gmatclub.com/forum/if-b-is-the- ... 27104.html
https://gmatclub.com/forum/ds-geometry- ... 28687.html
https://gmatclub.com/forum/in-triangle- ... 82671.html
https://gmatclub.com/forum/abcd-is-quad ... 31462.html

Hope it's clear.


Is it ok to infer that DC is the mid segment? DC can be parallel without being mid segment; In that case the answer will change


We can deduce that DC is the midsegment only after we combine the statements. At that point we know that C is the midpoint of EB and DC is parallel to AB, therefore, DC must be the midsegment. When considering the statements alone DC may or may not be the midsegment.
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In the triangle above, DC is parallel to AB. What is the len [#permalink]
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