[Grammar] -다가 to change actions

Verb1 -다가 Verb2

-다가 is a verb connector which connects two verbs.  It means the first action(verb1) has finished yet, but the action changes to the second action(verb2).  For example,

밥을 먹다가 나갔어요.  In the middle of eating, he went out. (the action of eating hasn’t finished)
잠을 자다가 깼어요. In the middle of sleeping, I woke up. (the action of sleeping hasn’t finished)
청소하다가 다쳤어요. In the middle of cleaning, I hurt myself. (the action of cleaning hasn’t finished)
발표를 하다가 잊어버렸어요. In the middle of presentation, I forgot. (the presentation hasn’t finished)
왜 말을 하다가 멈춰요? Why do you stop in the middle of speaking?
편지를 쓰다가 친구 생각이 났어요.  In the middle of writing a letter, I thought about my friend.
한국어를 공부하다가 너무 어려워서 포기했어요. In the middle of studying Korean, I gave up because it was too difficult.
시험을 보다가 잠이 들었어요.  In the middle of the test, I feel asleep. (Oh, no!!!!!!)
학교에 가다가 친구를 만났어요.  On the way to school, I met my friend.
집에 가다가 슈퍼에 들렀어요. On the way home, I stopped by a supermarket.