Tony Foster's Proof of Viviani's Theorem

What Might This Be About?

23 February, 2017, Created with GeoGebra

Viviani's Theorem

The sum of distances of a point inside an equilateral triangle or on one of its sides equals the length of its altitude.

Viviani's theorem

The theorem is named after Vincenzo Viviani (1622-1703).

Proof

Tony Foster's Proof of Viviani's Theorem

Acknowledgment

The above is a slight modification of Tony Foster's proof of Viviani's theorem.

 

Related material
Read more...

  • Equilateral and 3-4-5 Triangles
  • Rusty Compass Construction of Equilateral Triangle
  • Equilateral Triangle on Parallel Lines
  • Equilateral Triangle on Parallel Lines II
  • When a Triangle is Equilateral?
  • Viviani's Theorem
  • Viviani's Theorem (PWW)
  • Tony Foster's Proof of Viviani's Theorem
  • Viviani in Isosceles Triangle
  • Viviani by Vectors
  • Slanted Viviani
  • Slanted Viviani, PWW
  • Morley's Miracle
  • Triangle Classification
  • Napoleon's Theorem
  • Sum of Squares in Equilateral Triangle
  • A Property of Equiangular Polygons
  • Fixed Point in Isosceles and Equilateral Triangles
  • Parallels through the Vertices of Equilateral Triangle
  • |Contact| |Front page| |Contents| |Geometry|

    Copyright © 1996-2018 Alexander Bogomolny

    65649966