DS: Triangle

Question

I don't understand OA on this one.

gmat2me2 · Answer

I am getting B as answer...let me know if that is right i would then explain

chunjuwu · Answer

B = 90 degree

Angle ACB=60 degree, and angle CAB=30 degree, 

Hence, the triangle must not be isosceles triangle. 

A seems insufficient

chunjuwu · Answer

Go for B

angle B = 90 degree

Angle ACB=60 degree, and angle CAB=30 degree, 

Hence, the triangle must not be isosceles triangle. 

(1) seems insufficient

rxs0005 · Answer

B will disporve its not an isoceles triangle

so answer = B

subhen · Answer

It has to be B because the second stmt shows that the triangle abc is not isoceles triangle.

ashkg · Answer

Another vote for B.

In A , the angles of triangle ABC are not known to be equal or not.
In B, the angles are known and are 30,60

mirhaque · Answer

1 is suff too. 

acb=2adc.....1
acb=cad+adc.....2 (external angle equal two other internal angle)

combining 1 & 2 adc=cad. 
that means cd=ad. 

This goes to prove that triangle abc is not isosceles

gmat2me2 · Answer

I dont think you can use that theorem here simply because angle A is shared between the triangles . 

So your (2) in your explanation is a a doubt for me.

gmat2me2 · Answer

I get your point now mirhaque. the external angle of ADC is angle B and that should be suffiecient enough to say that A is also sufficient.....

ashkg · Answer

A is not sufficient.
I don't understand how you guys got A sufficient. B should be the answer.

gmat2me2 · Answer

Well the theorem the external angle of a triangle is equal to the sum of opposite angles is used here.

let acb = 2x while ADC = x 

since ACB=2x ==>> ACD=180-2x

In triangle ACD angles A + D +C =180

So we have C =180-2x D =x So angle A for ACD has to be x.

So it is isoceles

ashkg · Answer

The question is asking if trianlge ABC isosceles and not ACD.

gmat2me2 · Answer

Looks I have drifted to the other triangle :-D 

Anyway ...As per the question B would be enough.......Thanks ashkg.....

HongHu · Answer

For 1), if you draw a isoceles triangle with B a right angle and BA=BC, then you draw a nother isoceles triangle where AC=AD, then 1) would be satisfied. However you can also draw a right triangle ABC where BABC, and then still draw a triangle where AC=AD to satisfy 1). In other words 1) is not sufficient to determine whether ABC is isoleles.

DS: Triangle

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