어서 다치다

got hurt by doing X

-아/어서 names what caused the injury and 다치다 is getting hurt: 넘어져서 다쳤어요 'I fell and hurt myself', 눈을 맞아서 다친 'hurt after taking one to the eye'. Every line here reports an accident after the fact, and the cause is a specific mishap — slipping, spilling boiling water, going out on a bike. Note 다치다 is hurting yourself; hurting someone else is 다치게 하다.