These battles were proof for the British that the Patriots weren't just a ragtag team of rebels. This proved their worth and showed that the Patriots were formidable foes.
Battle of Saratoga
The Battle of Bunker Hill was a fierce battle that although the Patriots lost, the British Casualties was much higher than the Patriot casualties, and it proved the strength of our army to the British.
Battle of Yorktown
George Washington brought his army across the Delaware River overnight into an encampment of Hessions and attacked the morning after Christmas Eve, which surprised them and made the battle easier. The Patriots suffered no casualties.
Treaty of Paris of 1783
The Battle of Saratoga was a turning point in he war. The Hessonites & British were defeated and surrendered their arms to the Patriots.
Considered the last major battle of land in the Revolutionary War, the Continental Army, led by George Washington, won a decisive victory against the British Army (wikipedia.com)
The Treaty of Paris was a treaty created to end the war between Britain and France. In the terms of the treaty, France gave up its territories in mainland of America.