How are political speeches and persuasive writing similar? both provide amusement or enjoyment to an audience. both are not planned ahead of time. both try to convince people to take action or accept a certain belief. both explain ideas, processes, objects, or events.

The answer is: Both try to convince people to take action or accept a certain belief. 

Political speeches often disseminate a certain belief or idea to its audience. Oftentimes, it is trying to persuade the listener to act upon what is being said. In the same manner, persuasive writing presents certain idea and it convinces people to act upon the idea presented.