450: 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)?

sources:

Try to shade 1/3 of this triangle. How do you know it is 1/3? #mathchat #elemmathchat pic.twitter.com/KaLtPglBfV

— David Wees (@davidwees) May 2, 2015

@davidwees this may be more than you want pic.twitter.com/Azlkv1kwAw

— David Sawtelle (@davesawtelle) May 2, 2015