Knowing that I was late, I ran all the way.
Hoping to frighten the dog, he threw a stone at it.
Feeling rather ill yesterday, I decided to stay at home.
Thinking that the tin was empty, she threw it away.
(Note: In this type of structure, the present participle comes before the word to which it refers. Do not use this pattern unless it is clear that the participle expression refers to the subject of the following clause.