## File 10

**TRIANGLES ON REGULAR POLYGONS**

Excel file: 10.TrianglesOnRegularPolygons

Manipulating the file paper: 10.AttributesOfExcelFile10

General sharpest triangles paper: 10._SharpestApexObtuseTriangles

Part II of PwP concludes with a file that allows you to create an image of triangles embedded in a regular polygon by noting that three non-parallel lines will always create a triangle unless the three lines coincide at a single point. Even if they do coincide at a single point (all three pass through the peak vertex, for example), other lines parallel to the initial lines will create triangles. The Excel file is controlled by 4 parameters ** j**,

**,**

*k***and**

*v**, that define three non-parallel lines between vertices, together with click-boxes to control the image shown. All images created in Files 7, 8 and 9 can be recreated using this file by placing values in cells*

**w****,**

*j***,**

*k***and**

*v**or, alternatively, by placing equations in those cells.*

**w**The first paper provides a complete discussion of how to interpret and manipulate the file. The second paper, which examines sharpest triangles that are NOT isosceles or right, provides an example of the more general set of images that one can examine using this file.