Final answer:
Among the options, only BF3 has a trigonal planar geometry, as CO2 is linear, NH3 is trigonal pyramidal, and CH4 is tetrahedral.
Step-by-step explanation:
To determine which molecules have a trigonal planar geometry around each carbon atom, we need to consider the number and arrangement of electron groups around the central atom. A molecule with three electron groups adopts the positions of an equilateral triangle, with angles of 120° and all in the same plane, resulting in a trigonal planar shape. For instance, molecule BF3 exhibits this geometry as the fluorine atoms are positioned at the vertices of an equilateral triangle and all four atoms lie in the same plane.
Among the given options, CO2 (carbon dioxide) is linear, not trigonal planar, because it has two double bonds and no lone pairs on the carbon, NH3 (ammonia) has a trigonal pyramidal shape due to the presence of a lone pair on nitrogen, and CH4 (methane) is a tetrahedral molecule. Therefore, the molecule with trigonal planar geometry around each carbon atom is BF3 (boron trifluoride), agreeing with the provided reference information.