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

### Proof ### Acknowledgment

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

• 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
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