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Triangle ratio

grayfalcon89
in Mathematics

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This is a very easy problem.

 

Prove that if you connect midpoints of sides of any triangle to form a new triangle, the ratio of the area of the new triangle to the original triangle is 1:4.

 

Remember, proving means showing for all cases. It's easy to see this is true by equilateral triangle but that's not really proving. :)

A glib answer is that the new inner triangle is half the size in each linear direction of the outer one, is the same shape, so must be quarter the area.

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