＼ is listed under “shasen” (斜線; slanted line);
▽ is listed under “sankaku” (三角; triangle) along with bunch of other triangular symbols: △ ▲ ▼ ∵ and ∴.
Basically I only have to remember a couple of Japanese words that denote various shapes, and the IME gives me all the symbols it thinks I meant. There's also an added bonus for me: When I don't know the corresponding Japanese word for some shape, I can just look up the pronunciation of Chinese letters used in the corresponding Korean word, and it usually works. For example, triangle is written as 삼각 (samgak), whose Chinese letters are also 三角.
So convenient! :D
But it didn't have ♥ listed under ハート…. :-p