Ineed understanding participle and gerund phrases. could anyone try to explain them to me?

What element does susan b. anthony include in this passage to strengthen her argument?

What element of medieval literature does the disappearance of the sword into the lake represent?

Geoff bought a picture frame and took a picture with his parents because a) he wanted to be a notable athlete. b) he wanted to remember his trip always. c) he wanted to get into the hall of fame. d) he wanted a baseball player to sign it.