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Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees.

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amanvermagmat
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Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees. [#permalink] New post   07 Jun 2018, 05:24
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Is triangle ABC isosceles?

(1) Angle ABC is greater than 90 degrees.

(2) Median BD which joins AC at D, is NOT perpendicular to AC.
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SonalSinha803
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Re: Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees. [#permalink] New post   07 Jun 2018, 06:09
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According to statement 1, taking angle ABC greater than 90 or less than 90, both can give the probability of getting isosceles triangle as well as scalene. Hence, insufficient.

Statement 2 says, if the median is not perpendicular to AC, it is clear that the triangle is not isosceles. It is because a median of an isosceles triangle is always perpendicular to the opposite side.

Hence, sufficient.

Hence, option B.

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Re: Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees. [#permalink] New post   09 Jan 2021, 17:52
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Statement 1 is not sufficient on its own but it does give us valuable info: that the two equal sides COULD only be AB and AC.

You need that along with Statement 2 which tells you that the median line would be AD if it was perpendicular to BC. Hence you need both statements (C) to definitely answer the question as NO.
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Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees. [#permalink] New post   07 Jun 2018, 07:47
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SonalSinha803 wrote:
According to statement 1, taking angle ABC greater than 90 or less than 90, both can give the probability of getting isosceles triangle as well as scalene. Hence, insufficient.

Statement 2 says, if the median is not perpendicular to AC, it is clear that the triangle is not isosceles. It is because a median of an isosceles triangle is always perpendicular to the opposite side.
Hence, sufficient.
Hence, option B.


Here is a good example how the triangle is Statement 2 can be isosceles. See attachment.
Answer (C)
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1.png
1.png [ 10.72 KiB | Viewed 2545 times ]

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Re: Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees. [#permalink] New post   07 Jun 2018, 11:12
Hero8888,
Let angle b=120, angble a=20 and angle c=40.
This triangle will fullfill both statements but it is not isosceles

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Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees. [#permalink] New post   07 Jun 2018, 11:28
GYANENDRA88 wrote:
Hero8888,
Let angle b=120, angble a=20 and angle c=40.
This triangle will fullfill both statements but it is not isosceles

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Hi, GYANENDRA88

You are right in this part, but you have to understand DS format of GMAT. You have to prove that a statement is definitely YES or definitely NO. Getting clear "NO" makes statement valid too.
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Re: Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees. [#permalink] New post   07 Jun 2018, 18:25
Hero8888,
We can go with E

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Re: Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees. [#permalink] New post   07 Jun 2018, 21:22
SonalSinha803 wrote:
According to statement 1, taking angle ABC greater than 90 or less than 90, both can give the probability of getting isosceles triangle as well as scalene. Hence, insufficient.

Statement 2 says, if the median is not perpendicular to AC, it is clear that the triangle is not isosceles. It is because a median of an isosceles triangle is always perpendicular to the opposite side.

Hence, sufficient.

Hence, option B.

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If I'm not mistaken, the median of the unequal side of an isoceles triangle is perpendicular to the opposite side. Here we don't know which two sides are equal. So we really can't say. hence statement B is insufficient. Correct answer shoudl be E in my opinion.
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Re: Is triangle ABC isosceles? (1) Angle ABC is greater than 90 degrees. [#permalink] New post   29 Jun 2022, 16:01
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