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505-555 (Easy)|   Geometry|      
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danzig
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In the triangle above, DC is parallel to AB. What is the len Updated on: 05 Mar 2023, 09:46
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.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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75% (01:00) correct 25% (01:05) wrong based on 261 sessions

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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 5550 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
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Bunuel
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In the triangle above, DC is parallel to AB. What is the len 11 Jul 2013, 12:21
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danzig


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.
Show more

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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In the triangle above, DC is parallel to AB. What is the len 05 Mar 2023, 08:36
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Bunuel
danzig
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.
Show more

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 05 Mar 2023, 09:51
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Urvasi
Bunuel
danzig


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
Show more

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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