Final answer:
BHF₂ fits the criteria given by the student as it is polar and has trigonal planar molecular geometry. This molecule has a central boron atom bonded to three other atoms in a planar arrangement, which makes it polar due to the difference in electronegativity between boron and the atoms it is bonded to.
Step-by-step explanation:
The student is asking about the polarity and molecular geometry of certain compounds. To be both polar and have trigonal planar molecular geometry, a molecule must have a central atom with three pairs of electrons bonding to other atoms, and the molecular geometry should facilitate an imbalance in electron distribution.
Looking at each compound: H₂ is nonpolar and has linear molecular geometry; H₂O is polar but has bent molecular geometry; LiCl does not have a trigonal planar structure; BHF₂ contains polar bonds and has a trigonal planar electron-pair geometry and molecular structure as per example information provided. Therefore, BHF₂ fits the criteria of being polar and having trigonal planar molecular geometry.