If AB || DE and AB = 10, what is the length of DE?

The information tells us that ABC is similar to EDC..
Angles A=E; B=D (alternate angles)
Angle DEC=angle ACB ( opposite angles)
So ratio of sides is same...\(\frac{AB}{DE}\)=\(\frac{AC}{CE}\)=\(\frac{BC}{CD}\)..
We require to know any one of the ratio..

(1) BC = 6 and CE = 4
BC and CE are in different ratios so insufficient

(2) DC = 3 and CB = 6
.\(\frac{AB}{DE}\)=\(\frac{BC}{CD}\)....
.\(\frac{10}{DE}=[m]\frac{6}{3}\).....DE=10*3/6=5
Sufficient

B
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Hi chetan2u
What is the correct way of naming two similar training gles after we have recognized that they are similar.
I got A as I named the triangles
CAB and CDE

Thanks

Posted from my mobile device
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You have to name as per the angles that is why I mentioned angles A=E, B=D and C=C
So name it in similar way..
ABC and EDC or CAB and CED and so on
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Our video on Similar Triangles suggests a way to determine which sides correspond by labeling the angles differently.



Cheers,
Brent

Let's first add the given information (and their implications) to the diagram

If AB || DE, we know that ∠BAC = ∠CED and ∠ABC = ∠DCE
Also, since vertically opposite angles are equal, we know that ∠ACB = ∠DCE



Now that we've identified 3 pairs of EQUAL angles, we can conclude that the two triangles are SIMILAR
So, we need to determine which sides are corresponding.
Notice that side AB and side DE BOTH lie between the angles denoted by a star and a square.
This means that side AB corresponds with side DE (denoted by BLUE lines)


Likewise, side BC and side CD both lie between the angles denoted by a circle and a square.
This means that side BC corresponds with side CD (denoted by RED lines)


Finally, side AC and side CE both lie between the angles denoted by a circle and a star.
This means that side AC corresponds with side CE (denoted by GREEN lines)


Now onto the question!!!!

Target question: What is the length of DE?

Statement 1: BC = 6 and CE = 4
Add this info to the diagram:


Notice that we don't know the lengths of two corresponding sides.
As such, we can't determine the magnification factor of the two similar triangles (see the video below for more information about magnification factor)
As such, there's no way to determine the length of side DE
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: DC = 3 and CB = 6
Add this info to the diagram:

Notice that DC and CB are corresponding sides.
So, the magnification factor of the similar triangles = 6/3 = 2
In other words, ∆ABC is 2 times the size of ∆EDC
So, if side AB = 10, then side DE (the side that corresponds with side AB) must have length 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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