Triangle ratio

[grayfalcon89]

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.

[Garfield]

Quite easy to prove with similar triangles.

[Neil9327]

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.