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Common Intersection point of Medians in a triangle

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by goelmohit2002 » Wed Sep 16, 2009 12:32 pm
Hi All,

Can someone please tell is the property that medians of a triangle drawn from all three sides meet at a point that divides all the medians in 1:2 ratio and is tested in GMAT ?

if yes then can someone please point me to a problem that tests this concept....

I checked Manhattan strategy guide of geometry....

But it does not talk about this median concept.... does it mean that this median property is not in the course of GMAT ?

Thanks
Mohit
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Re: Common Intersection point of Medians in a triangle

by Brent@GMATPrepNow » Wed Sep 16, 2009 9:38 pm
goelmohit2002 wrote:Hi All,

Can someone please tell is the property that medians of a triangle drawn from all three sides meet at a point that divides all the medians in 1:2 ratio and is tested in GMAT ?

if yes then can someone please point me to a problem that tests this concept....

I checked Manhattan strategy guide of geometry....

But it does not talk about this median concept.... does it mean that this median property is not in the course of GMAT ?

Thanks
Mohit
Test-takers are not required to know any theorems related to medians of triangles. In fact, you don't even need to know what a median is. (BTW, a median is a line that connects a vertex of a triangle to the midpoint of the side opposite that vertex).
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Re: Common Intersection point of Medians in a triangle

by goelmohit2002 » Wed Sep 16, 2009 9:42 pm
Brent Hanneson wrote:
goelmohit2002 wrote:Hi All,

Can someone please tell is the property that medians of a triangle drawn from all three sides meet at a point that divides all the medians in 1:2 ratio and is tested in GMAT ?

if yes then can someone please point me to a problem that tests this concept....

I checked Manhattan strategy guide of geometry....

But it does not talk about this median concept.... does it mean that this median property is not in the course of GMAT ?

Thanks
Mohit
Test-takers are not required to know any theorems related to medians of triangles. In fact, you don't even need to know what a median is. (BTW, a median is a line that connects a vertex of a triangle to the midpoint of the side opposite that vertex).
I guess one property I have commonly seen in GMAT questions is median of a isoceles triangle...

1. it bisects the angle.
2. bisects the base
3. is perpendicular to the base..

Please tell if I am wrong here.

But I am not sure about the property of medians intersecting at the point which divides the medians in 1:2 ratio.
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by Brent@GMATPrepNow » Wed Sep 16, 2009 9:46 pm
Sure, it's useful to know those points about isosceles triangles, but you can deduce those in other ways (congruent triangles).

What I was getting at is that you don't need to know the definition of a median and you don't need the theorem regarding the 2:1 ratio.
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by goelmohit2002 » Wed Sep 16, 2009 9:49 pm
Brent Hanneson wrote:Sure, it's useful to know those points about isosceles triangles, but you can deduce those in other ways (congruent triangles).

What I was getting at is that you don't need to know the definition of a median and you don't need the theorem regarding the 2:1 ratio.
Hi Ben,

Thanks. Is Congruent triangles concept tested in GMAT....as far as I know only similarity is tested.
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by Brent@GMATPrepNow » Wed Sep 16, 2009 10:08 pm
goelmohit2002 wrote:
Brent Hanneson wrote:Sure, it's useful to know those points about isosceles triangles, but you can deduce those in other ways (congruent triangles).

What I was getting at is that you don't need to know the definition of a median and you don't need the theorem regarding the 2:1 ratio.
Hi Ben,

Thanks. Is Congruent triangles concept tested in GMAT....as far as I know only similarity is tested.
Tricky question. While it isn't necessary to explicitly prove congruency, I believe that you should be aware of the fact that, given the lengths of all three sides of a triangle, there is only one triangle possible that has these lengths. Similarly, if you know the lengths of two sides and you know the angle between these sides, then there is only one possibility for the placement/length of the third side. I believe that these concepts are tested in some way or another on the GMAT. For example, if we know that two sides of a triangle have length 3 and 4 and the angle between them is 90 degrees, we are implicitly using the notion of congruency when we determine the length of the 3rd side (hypotenuse) when we use the Pythagorean theorem. We are assuming that there is only one possible length for the 3rd side, given that we already know two sides and the angle between them.
Does this mean the GMAT tests congruency? Maybe. It depends on how you define the notion of a concept being tested.
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