TITLE: Does "triangle" in English exclude degenerate triangles?
QUESTION [5 upvotes]: Just for fun read few problems on the projeteuler.net website.
Number 276 found interesting:

Consider the triangles with integer sides a, b and c with a ≤ b ≤ c.
  An integer sided triangle (a,b,c) is called primitive if gcd(a,b,c)=1.
  How many primitive integer sided triangles exist with a perimeter not
  exceeding 10 000 000?

Question:

Does the definition "triangle" in English also enforces the following condition?
a + b > c

REPLY [2 votes]: In some mathematical English, a triangle means exactly what it did 2,300 years ago:

"A triangle is plane figure bounded by three straight lines." (A Text-book of Euclid's Elements, Hall & Stevens, 1888).

This definition seems unclear. 
But later, Proposition 20 clarifies it (emphasis added):

"Any two sides of a triangle are together greater than the other third side." (ibid.)

However, the articles https://en.wikipedia.org/wiki/Triangle_inequality and https://en.wikipedia.org/wiki/Normed_vector_space contradict one another: the latter includes equality.
But, I think, most (English) mathematicians would agree with the latter, and disagree with Euclid, and will allow degenerate triangles to partake in the so-called triangle inequality.