Proof
Let point C be the origin of Cartesian coordinate.
Then the equation for segment AD is y=1-x, and eq. for segment CE is y=x/2.
Since point G is the intersection of these two segments, solving the two equations, we get G=(2/3,1/3).
Thus CG=CE*(2/3)/2=CE/3. Since the whole shape has rotational symmetry, HE=CG=CE/3.
Consequently GH=CE-CG-HE=CE/3. Therefore, CG=GH=HE. ■
이산구조 ppt에 저런 그래프가 나오길래
하라는 공부는 안하고 'ㅅ'
A little bit more beautiful proof
Draw a segment from G which is parallel to DF. Let's call the intersection of the segment and HF point I.
Then, CDG≡GIH≡EBH because □ABFD is a parallelogram. Therefore, CG=GH=HE. ■
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