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How do cis and trans isomers form in cyclopropane rings?

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Two diagrams show the three-dimensional structure of a methane molecule: panel A uses a ball-and-stick model with a central carbon atom connected to four hydrogen atoms in a tetrahedral arrangement, while panel B illustrates the bond angle of 109.5 degrees and bond length of 1.09 angstroms between carbon and hydrogen atoms. — isomerism Tetrahedral geometry of methane: (A) stick-and-ball model and (B) diagram showing bond angles and distances. (Plain bonds represent bonds in the plane of the image; wedge and dashed bonds represent those directed toward and away from the viewer, respectively.)

In cyclopropane rings, cis and trans isomers are a type of stereoisomerism where substituents are positioned on either the same (cis) or opposite (trans) sides of the plane defined by the three-membered ring.1

Unlike some larger cycloalkanes, cyclopropane is necessarily flat because three points determine a plane, meaning there is no possibility for out-of-plane distortion. Furthermore, because the ring is rigid, there is no rotation about the carbon-carbon bonds that could interconvert these isomers. Consequently, cis- and trans-cyclopropane derivatives are not conformational isomers; they are distinct compounds with their own unique physical properties, such as different boiling points. Because these isomers cannot be interconverted at room temperature, changing from one form to the other would require the breaking and reforming of chemical bonds.231