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Subject: "A property of equilateral triangles"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #394
Reading Topic #394
mffsilva61
Member since Apr-8-10
 Apr-08-10, 07:01 AM (EST)
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"A property of equilateral triangles"
 
   This is a very beautiful property of equilateral triangles.
Let ABC an equilateral triangle, and M any point inside it. Divide the triangle in six rectangular triangles joining the point M to A, B, C, Ma, Mb and Mc, where Ma, Mb and Mc are the pedal points of M. The property to prove is that
Area(MAMc) + Area(MBMa) + Area(MCMb) = Area(MBMc) + Area(MCMa) + Area(MAMb)
that is, green and blue areas in the attached figure are equal.
I have not found this property in this site, and I discovered by myself an elegant demonstration for it. Do you think it deserves a place here, Alex?
fernando

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alexbadmin
Charter Member
2490 posts		 Apr-08-10, 11:41 AM (EST)
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1. "RE: A property of equilateral triangles"
In response to message #0
 
   > Do you think it deserves a place here,

Absolutely. A very nice property of equilateral triangles. I have made a page for it:

https://www.cut-the-knot.org/Curriculum/Geometry/EqualAreasInEquilateralTriangle.shtml

Many thanks. Let me know if your demonstration is different from mine. Also, do you have a reference to point to?

Thank you again,
Alex


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