The word for cutting or dividing something into two equal parts is bisect.
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To cut or divide into two parts., To divide into two equal parts.
To "bisect" something is to divide it into two parts. Usually these parts are equal.
Two equal parts.
No, there is not. When you cut a shape with only one cut, you are creating two parts. In order to make four parts (no matter what the shape is), you would need to make two cuts.
Halve