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

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Are two triangles congruent? (I) They are both equilateral [#permalink]

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28 Jun 2009, 05:04
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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!!
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Retired Moderator
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Kudos [?]: 1218 [0], given: 157

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GMAT 1: 680 Q48 V34
Re: Are two triangles congruent?? [#permalink]

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28 Jun 2009, 05:20
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!!

If two triangles have two sides equal then its obvious that the third side is also equal, hence II is sufficient for me .. Am I wrong??
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Re: Are two triangles congruent?? [#permalink]

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28 Jun 2009, 13:18
I is sufficient. It is clear.

Bu II is insufficient. Because it only gives us the base and the heights equality. But we do not know the other 2 sides. Think this 2 triangles.
- Base is 3, height is 4 and the hypotenus is 5.
-Base is 3, height is 4 but the other sides are (root 73) / 2
These two triangles have the same base and height but are different.

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Re: Are two triangles congruent?? [#permalink]

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28 Jun 2009, 14:08

1) Not sufficient, all equilateral triangles are similar, but not congruent. ie sides need not be of the same length

2) not sufficient. Height and one side being same doesn't mean they are always congruent, the angles may be different. Try to do it using rules of congruency, this statement doesn't guarantee that any of those rules is being satisfied.

Both combined, equilateral triangles having any side same will always be congruent. so ans is C.

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Re: Are two triangles congruent?? [#permalink]

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28 Jun 2009, 14:36
I did not know the exact meaning of congruent. I confused it with similar. If congruent means exactly the same, than C is clear.

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Re: Are two triangles congruent?? [#permalink]

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28 Jun 2009, 20:13
Now I came to know where did I go wrong??

I was taking these as right triangles as the height was mentioned, I know its stupid but my mind went directly to right triangle and started assuming that II is sufficient as the hypotenuse will be same if the base and height is same.

Its a good lesson for me!! Thanks to all of you for your input!!
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Re: Are two triangles congruent?? [#permalink]

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29 Jun 2009, 15:07
what is the OA?
If one is right angled triangle and other is not, will they be congruent?

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Re: Are two triangles congruent?? [#permalink]

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29 Jun 2009, 15:30
Two triangles are congruent when they are exact mirror images of each other, although, one of them may be rotated so that it doesnt resemble the other at the first glance, but that wouldnt affect the congruent property

The basic connection is that Corresponding sides are equal for both triangles (that implies that corresponding angles too must be equal)

You can look up for the 5 rules of congruency at http://www.onlinemathlearning.com/congr ... ngles.html, if any one of these is satisfied, the triangles are congruent

If only angles are equal, the triangles are similar, but sides need not be equal. ie, one can be an enlarged image of the other.

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Re: Are two triangles congruent?? [#permalink]

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29 Jun 2009, 17:02
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??   [#permalink] 29 Jun 2009, 17:02
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