Which one of these battles of the american revolution provided the turning point of the war, in which the french joined in support of the colonies?

That would be the battle of Saratoga. The battle of Saratoga was a turning point in the war and convinced the French government to recognize the colonies' cause, leading to France entering the war as America's ally. This later became crucial during the Siege of Yorktown, when Washington gave orders French Commander Rochambeau to make sure France held the Chesapeake Bay. Ultimately, France was able to do this, trapping Cornwallis' British army by sea. Cornwallis could not escape. Trapped by the French navy by sea and Washington's Continental Army by land, Cornwallis was forced to surrender, ending the American Revolutionary War.

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