Solved: an accepted full claim settles the problem, whether or not three distinct collinear points count as a triangle. Bloom's catalog labeled the problem OPEN (page last edited 16 October 2025). Plasma AI proves that every two-coloring of the plane has a monochromatic congruent copy of every triangle, collinear triples of distinct points included, except at most one, which is then equilateral; that claim, on the Plasma AI page, is accepted on this corpus's rebuild, Comparator check and kernel replay of its Lean formalization, a graded review of the formal statements and the sign-off of Jacob Parish at Plasma AI. Its prose argument has an independent whole-conclusion review and a separate passing grade. Three results decide the question for particular triangles and are recorded as partial claims. Shader's refereed theorem of 1976 shows that every right triangle, and every triangle of two further one-parameter families, has a monochromatic congruent copy in every two-coloring of the plane. It is on Shader 1976, accepted on the refereed publication alone. The 1975 colloquium paper of Erdős, Graham, Montgomery, Rothschild, Spencer and Straus gives further triangle families. It is on EGMRSS 1975 with status claimed. The paper appeared in a proceedings volume. Currier, Moore and Yip's refereed theorem of 2024 shows that three equally spaced collinear points, and every $(\alpha,2\alpha,x\alpha)$ triangle with $1\le x\le3$, appear monochromatically. It is on Currier, Moore and Yip 2024, accepted on the refereed publication alone.