tag:blogger.com,1999:blog-6933544261975483399.post2738840992844125072..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Problem 402. Hexagon, Triangle, Centroid, Parallel, Congruence, SimilarityAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-6933544261975483399.post-48875030380776926092021-08-03T08:17:31.729-07:002021-08-03T08:17:31.729-07:00Interesting about the areas, but the result about ...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.htmlMdeVhttps://www.blogger.com/profile/04911141015765114466noreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-30690832899778021172009-12-12T09:14:01.811-08:002009-12-12T09:14:01.811-08:00We see that
XH=(XB+XC+XD)/3
XG=(XB+XC+XA)/3
XK=(...We see that <br />XH=(XB+XC+XD)/3<br />XG=(XB+XC+XA)/3<br />XK=(XD+XE+XF)/3<br />XL=(XE+XF+XA)/3<br />and HG=(XH-XG,YH-YG)=(XD-XA,YD-YA)/3<br />LK=(XK-XL,YK-YL)=(XD-XA,YD-YA)/3<br />etc.<br />And my question for this picture - prove <br />area hexagon ABCDEF/area hexagon GHJKLM = 9/4Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-70337734923877752552009-12-12T00:59:08.542-08:002009-12-12T00:59:08.542-08:00the affix of triangle ABC centroid G is
g=(a+b+c)/...the affix of triangle ABC centroid G is<br />g=(a+b+c)/3<br />then<br /> 3(h-g)= b+c+d-a-b-c= d-a<br /> 3(k-l)= d+e+f-e+f+a= d-a<br />this means that GH=LK and GH // LK<br />.........Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6933544261975483399.post-30954380793246308172009-12-11T10:47:16.326-08:002009-12-11T10:47:16.326-08:00My problems for this picture.
Proff
1)Area hexago...My problems for this picture.<br />Proff <br />1)Area hexagon ABCDEF/ Area hexagon GHJKLM = 9/4.<br /><br />2) Area polygon ABCDE/ Area polygon GHJKL = 117/32.<br /><br />2) Area polygon ABCD/ Area polygon GHJK = 9.Anonymousnoreply@blogger.com