proved
To show something is true by using good evidence.
To prove something means to show that it's true using evidence, logic, or demonstration. When a mathematician proves a theorem, she uses logical steps that anyone can follow to see why it must be true. When a detective proves who committed a crime, he gathers evidence that eliminates all doubt. When you prove you can handle more responsibility, you demonstrate through your actions that you're ready for it.
The past tense is proved or sometimes proven. You might say “She proved her point” or “She has proven herself reliable.” Both forms work, though proved is more common as the simple past tense.
Proving something requires more than just claiming it's true. If your friend says the school cafeteria serves pizza on Fridays, you might believe them. But if someone doubts it, you could prove it by showing them the cafeteria menu or walking there on Friday to see for yourself. Scientists prove their ideas through careful experiments. Lawyers prove their cases with witnesses and evidence.
Sometimes people use prove to mean that something turns out a certain way: “The difficult hike proved too challenging for the younger kids.” Here, the hike revealed or demonstrated its difficulty through actual experience.