Assignment6

The question I choose for assinment 1 is below.

I made the desiered two triangles.

The yellow one is the first triangle and the green one is the second trianlge.

AD, BE, and CF are medians of the first triangles.

I draw the second triangle by drawing three circles each of which has a radius that has equal length to a median of the first triangle.
BE = HG
CF = IH

These two triangle are neither congruent nor similar.

They do not have same area nor same perimeter.

What I found about the relatonship of the two triangles is that the ratio of ares is a constant.

See this fact by clicking here.

Proove what I found, the ratio of areas is a constant.

First of all, put one median of the first triangle together to the side of the second triangle that has same length of the median.

and call the intersection of AB and HD as J.

AJD + HJF = 1/2 ABC (because HJF = DJB)

AHF = 1/4 ABC (because AHF =BEF = 1/2 EAB = 1/4 ABC)

So,

AHD = AJD + HJF + AHF = 1/2 ABC + 1/4 ABC = 3/4 ABC

So, AHD =3/4 ABC

Thus, the ratio of the two triangle is a constant.

ABC/AHD = 4/3.

return