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Are two triangles congruent? (I) They are both equilateral

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Hussain15
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Are two triangles congruent? (I) They are both equilateral [#permalink] New post   28 Jun 2009, 05:04
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E

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Are two triangles congruent?

(I) They are both equilateral triangles
(II) They both have equal bases and equal heights

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Re: Are two triangles congruent? (I) They are both equilateral [#permalink] New post   08 Feb 2011, 11:41
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Two triangles are said to be congruent if they can overlap each other precisely :)

Statement 1:

They can be both equilateral triangles but unless they have the same dimensions they will not overlap each other perfectly. So the statement is not sufficient :)

Statement 2:
Two triangles sharing the same base and same altitude (height) needn't be congruent.
E.g It two triangle ABC and PBC share the base BC, and ABC is an obtuse angle triangle, ABC and PBC will have the same base and height but they will not overlap each other perfectly.

Thus Insufficient

Statement 1 & 2
If the triangles share the base and are both equilateral, it shows that all sides are equal... Thus they will overlap each other perfectly

Sufficient!
Ans: 'c'
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Re: Are two triangles congruent? (I) They are both equilateral [#permalink] New post   18 Feb 2011, 12:50
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Statement 2 in this question doesn't make sense. A triangle doesn't have *one* base and one height; it has *three* sides you could choose as a base, and three heights each corresponding to a base. So it makes no sense to say 'the height of triangle A is equal to the height of triangle B'; triangles have more than one height.

One could just as easily interpret the statement "Triangle A and Triangle B have bases of equal length" to mean that all three of the bases of Triangle A are equal in length to a base of Triangle B, and that the two triangles thus have sides of equal length, making the two triangles congruent. That would make Statement 2 sufficient alone.

It's a terribly worded question in any case; where is it from?

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Re: Are two triangles congruent? (I) They are both equilateral [#permalink] New post   29 Jun 2009, 17:02
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Hussain15 wrote:
Are two triangles congruent?
(I) They are both equilateral triangles
(II) They both have equal bases and equal heights

I have a few points to discuss on this issue, but I will wait for some answers initially!!


I'm curious where the question is from. The wording is terrible - Statement 2 doesn't actually make sense, or at least it doesn't mean what I expect the question writer intended. You would never see a question written this way on a real GMAT. A triangle doesn't have a single base; any side can be a base. Nor does a triangle have a single height; heights are relative to a chosen base, and most triangles have three heights of different lengths. To say that two triangles have 'equal bases' (plural) means they have 'equal sides', which of course makes them congruent. I'm guessing that's not what the question writer meant, however.
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Re: Are two triangles congruent? (I) They are both equilateral [#permalink]
29 Jun 2009, 17:02
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