Is CB||ED? (1) ABC and AED are both isosceles triangles (2) C = E

Question

https://gmatclub.com/forum/download/file.php?id=71625 Is CB || ED? (1) ∆ABC and ∆AED are both isosceles triangles (2) ∠C = ∠E QY581Gp.png

SajjitaKundu · Answer

can we not deduct from the diagram that angle(CAB) = angle (EAD)??
Can someone give the solution?
I got C based on the above assumption.

PKN · Answer

This question asks us to check the parallel line & it's transversal.

Here, BC & ED are the lines to be checked for parallelism and CD & BE are the transversals.

BC|| ED when the alternate angles in the given figure are equal. i.e,  \angle{CBA} = \angle{AED}  and  \angle{ACB} = \angle{ADE}

Question stem: BC || ED? (Y/N)

Statement1:-∆ABC and ∆AED are both isosceles triangles

we only know that vertically opposite angles are equal, i.e,  \angle{CAB} = \angle{EAD}  and we don't know their measure in degrees.-----------(a)

Remaining two angles of both the isosceles triangles can have 'n' no of possible combinations.

hence st1 is not sufficient.

Statement1:-∠C = ∠E --------(b)

In ∆ABC and ∆AED, from (a) and (b) ,we have  \angle{CBA} = \angle{ADE}

So, we can't say whether  \angle{CBA} = \angle{AED}  and  \angle{ACB} = \angle{ADE}  or not.

Hence statement2 is not sufficient.

(1)+(2), we have

(i) ∠C = ∠E
 (ii) \angle{CAB} = \angle{EAD} 
 (iii)  \angle{CBA} = \angle{ADE} 
 (iv) Both the triangles are isosceles; it has 2 cases:-

1.when  \angle{E} = \angle{D}

then  \angle{C}=\angle{D}  &  \angle{B}=\angle{E}

So, Is BC || ED? Yes (As alternate angles are found equal)

2.when  \angle{E}=\angle{A}

then  \angle{C}
eq\angle{D}  &  \angle{B}
eq\angle{E}

So, Is BC || ED? No (As alternate angles are not equal)

Ans. E

BrentGMATPrepNow · Answer

Many people will feel that the correct answer is C, but it's E

Keep at it!

Cheers,
Brent

sandman13 · Answer

Okay, so this is tricky.

Basically, the triangles are isosceles but it is not given which sides are equal. So assuming angle C = angle B would be incorrect. 
Similarly, assuming angle E = angle D would be incorrect as well. 
They  could  be equal. 
Statement 1 is insufficient.

Statement 2 by itself is pretty clearly insufficient.

Let's add both of these together and see what happens. 
It eventually boils down to the reasoning used in statement 1 where there are two cases, one in which the lines are parallel and one in which they are not.

So E is the answer in my opinion.

GMATGuruNY · Answer

Statements combined:
Case 1:
 https://i1262.photobucket.com/albums/ii605/gmatguruny/triangles%20and%20parallelism_case%201_zps4waibbnr.png 
In this case, ∠B = ∠E and ∠C = ∠D, so CB || ED.

Case 2: 
 https://i1262.photobucket.com/albums/ii605/gmatguruny/triangles%20and%20parallelism_case%202_zps7j93g3a3.png 
In this case, ∠B ≠ ∠E and ∠C ≠ ∠D, so CB is NOT parallel to ED.

Since the answer to the question stem is YES in Case 1 but NO in Case 2, INSUFFICIENT.

E

BrentGMATPrepNow · Answer

Target question :    Is CB || ED?

Let's jump straight to....

Statements 1 and 2 combined    
Statement 1 tells us that ∆ABC and ∆AED are both isosceles triangles
Statement 2 tells us that ∠C = ∠E

Let's start with 2 identical isosceles triangles:
 https://i.imgur.com/IQe4Cwq.png

If we arrange the triangles this way....
 https://i.imgur.com/kXd1PzU.png 
....we can see that the answer to the target question is  YES, side CB IS parallel to side ED

HOWEVER, if we arrange the triangles this way....
 https://i.imgur.com/dnWBzLC.png 
....we can see that the answer to the target question is  NO, side CB is NOT parallel to side ED

Since we cannot answer the  target question  with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

chetan2u · Answer

An immediate observation..

We can easily have both statements true and have the top triangle tilted on top of the bigger one...
So we cannot restrict the two triangles in any particular position, and thus we can not say anything about CB||ED

E

bumpbot · Answer

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Is CB||ED? (1) ABC and AED are both isosceles triangles (2) C = E

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Is CB||ED? (1) ABC and AED are both isosceles triangles (2) C = E

Prep Toolkit

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