Math Arguments

One-third of a triangle

You've been asked to shade one-third of this triangle.




And how do you know?

Here's a response:

• Is this a valid way to get one-third of the triangle?


• Does this technique require that we stipulate a right triangle?


• Does this technique require that we stipulate an isosceles one?


• Do the lines have to be parallel to each other?


• Do the lines have to be parallel to a side for this to work? 


• Perpendicular to a side for this to work?

• How might we generalize this method (if it can be generalized)?