Apart from tetrahedral geometry, another possible geometry for CH₄ is square planar with four H atoms at the corners of the square and the C atom at its centre. Explain why CH₄ is not square planar?

Here 1 s orbital & 3 p orbitals undergo hybridization to form sp³ hybrid orbitals .Hence, carbon atom undergoes sp³ hybridization in CH₄ molecule and takes a tetrahedral shape.

For a square planar shape, the hybridization of the central atom has to be dsp₂, ie, 1 s orbital, 3p orbitals & 1 d orbitals have to undergo hybridization .However, an atom of carbon does not have d-orbitals to undergo dsp² hybridization. Hence, the structure of CH₄ cannot be square planar.
Moreover, with a bond angle of 90° in square planar, the stability of CH₄ will be very less because of the repulsion existing between the bond pairs. Hence, VSEPR theory also supports a tetrahedral structure for CH₄.