Proposed Problem
Click the figure below to see the complete problem 402 about Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity.
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Complete Problem 402
Level: High School, SAT Prep, College geometry
Thursday, December 10, 2009
Problem 402. Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity
Labels:
centroid,
congruence,
hexagon,
parallel,
similarity,
triangle
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My problems for this picture.
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1)Area hexagon ABCDEF/ Area hexagon GHJKLM = 9/4.
2) Area polygon ABCDE/ Area polygon GHJKL = 117/32.
2) Area polygon ABCD/ Area polygon GHJK = 9.
the affix of triangle ABC centroid G is
ReplyDeleteg=(a+b+c)/3
then
3(h-g)= b+c+d-a-b-c= d-a
3(k-l)= d+e+f-e+f+a= d-a
this means that GH=LK and GH // LK
.........
We see that
ReplyDeleteXH=(XB+XC+XD)/3
XG=(XB+XC+XA)/3
XK=(XD+XE+XF)/3
XL=(XE+XF+XA)/3
and HG=(XH-XG,YH-YG)=(XD-XA,YD-YA)/3
LK=(XK-XL,YK-YL)=(XD-XA,YD-YA)/3
etc.
And my question for this picture - prove
area hexagon ABCDEF/area hexagon GHJKLM = 9/4
Interesting about the areas, but the result about the formed hexagon having opposite sides equal & parallel can be generalized for 2n-gons as shown here: http://dynamicmathematicslearning.com/octagoncentroids.html
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