Is triangle ABC an isosceles?

Question

Screen Shot 2012-05-08 at 1.05.37 PM.png Note: Figure not drawn to scale. Is triangle ABC an isosceles? (1) AB/BC = 2 (2) x≠y

Bunuel · Accepted Answer

Your reasoning is correct answer should be C, not E. Is triangle ABC an isosceles? Screen Shot 2012-05-08 at 1.05.37 PM.png (1) AB/BC = 2 --> AB eq{BC} . Not sufficient on its own. (2) x≠y --> AB eq{AC} . Not sufficient on its own. (1)+(2) Since AB eq{BC} and AB eq{AC} , then the only way ABC to be isosceles is when AC=BC . But in this case as given that AB=2BC then AB=BC+BC=BC+AC which is not possible because the length of any side of a triangle must be smaller than the sum of the other two sides . So, AC eq{BC} , which means that ABC is not isosceles. Sufficient. Answer: C.

Ljchen121 · Answer

I thought it was C, because the only way for the triangle to be isosceles given both conditions is for BC = AC , and that's not possible because side AC + BC (assuming they are the same length) would equal AB. And the third side of the triangle must be greater than the sum of the other two sides or less than the difference of the other two sides. So given both conditions, should we be able to say for sure that the triangle is not isosceles?

The OG says it's E though. Please help.

The OG says it's E though. Please help.

sub3108 · Answer

Initially tricked upon thinking it is E. Thanks Bunuel for the explanation.

narangvaibhav · Answer

Answer should be E
even if we cosider both 1) & 2) consider the below examples:

Case 1--> x= 30, y=100 & third angle= 50
Case 2--> x=45, y=90 & third angle =45

here both 1) & 2) are satisfied but there is contradiction in result, i.e. in one case traingle is issoceles, in other it is not, for the same conditions. Hence E

Bunuel · Answer

When considering the statements together the red scenario is not possible. If x=z then it would mean that AC=BC. But in this case as given that AB=2BC then AB=BC+BC=BC+AC which is not possible because the length of any side of a triangle must be smaller than the sum of the other two sides.

vibhav · Answer

intense reasoning guys! I picked E and didnt test the problem from the length of sides perspective. looked only at the angles.

saggii27 · Answer

can side AB=AC from 1st statement by making x=y?

Bunuel · Answer

Yes, for (1) it's possible that AB=AC as well as it's possible that AB#AC, so the first statement is not sufficient.

Shobhit7 · Answer

Hi,

Basis Statement 1 alone: Given ratio of two sides of a triangle AB:BC as 2:1 and Triangle Inequality, how is it possible to create an isoslece triangle?

Please advice.

Bunuel · Answer

2 - 2 - 1 MSP19491ghda5g6di30c1c600005766b2539c6cd6he.gif

Nunuboy1994 · Answer

St 1

This statement just tells us that angle A = 2Y however we don't know for certain whether this is an isosceles because

2(50) + 50 + x =180
 x =30

Or you could have an isosceles

2(45) + 45 +45 =180 
 
But we can't make that decision unless we have more info

Insuff

St 2

Not necessarily

St 1 and St 2

If x cannot equal y then we cannot have an equilateral

C

CEdward · Answer

Is this an OG question?

Can we reason this way?

Let's assume angle A is z.

St1. AB/BC = 2...this implies y = 2z...but insufficient b/c we don't know whether x = y
St2 x cannot equal y...insufficient b/c we don't know whether x = z

Combined:

3 angles - x, y, and z...each of which are distinct. Hence, ABC is NOT isosceles.

C.

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Is triangle ABC an isosceles?

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Is triangle ABC an isosceles?

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