triangles formed by joining Midpoints of a triangle

[goelmohit2002]

Hi All,

Can someone please tell is the property that

"when we join mid points of a triangle, then triangles that are formed are similar to original triangle and have 1/4th the area"

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 concept....does it mean that this mid point property of triangle is not in the course of GMAT ?

Thanks
Mohit

[mnyeri]

It can be deduced very easily.

Area of Triangle = A = 1/2 ( b*h)
Smaller traingle created using mid points implies that Height and Base of smaller triangle are each half that of full triangle.
Hence area of smaller traingle = a= 1/2 ( b/2* h/2) = bh/8

a/ A = (bh/8)* (bh/2) = 2/8 = 1/4


Hope this helps

[goelmohit2002]

It can be deduced very easily.

Area of Triangle = A = 1/2 ( b*h)
Smaller traingle created using mid points implies that Height and Base of smaller triangle are each half that of full triangle.
Hence area of smaller traingle = a= 1/2 ( b/2* h/2) = bh/8

a/ A = (bh/8)* (bh/2) = 2/8 = 1/4


Hope this helps

Thanks mnyeri.

Thanks Helps !!!

[Ben Ku]

Can someone please tell is the property that

"when we join mid points of a triangle, then triangles that are formed are similar to original triangle and have 1/4th the area"

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

If this property is tested on the GMAT, it will be in an area problem involving triangles, or a similar triangle problem. You should not have to know this specific property to solve such problems.

thanks, mnyeri for the proof of the property.