Isosceles Triangle ? I think the proposed answer is wrrong

[fatnanikishan]

I faced this problem in Manhatten test, I am not able to paste the image.

Question: For Triangle ABC,

Angle ABC = X

Angle ACB = Y

Is Triangle ABC Isosceles traingle:

a. X <> Y (X is not equal to Y)

b. AB = 2 BC


The answer proposed is (C)

I think Answer shall be (B), based on the property of inequality of triangle,

AB-BC < AC and AB > BC + AC,

this means BC < AC < BC, which is not possible and hence this cannot be a triangle.

Please do let me know where I am wrong.

[mschwrtz]

I'll bet that you could take a make a triangle out of a 10cm straw and two 20cm straws.... In fact, I'll bet that you can imagine such a triangle right now.

The trouble is with your claim that AB > BC + AC. This does not express a property of a triangle. In fact it contradicts your claim that AB-BC < AC, not just for this triangle but for every conceivable triangle.
The correct formulae areAB-BC < AC and AB > BC - AC. You can see that these are equivalent. The two expressions of the triangle inequality theorem are just that, two expressions of the same theorem