The type of ligand significantly influences the geometry of metal complexes by determining both the number and arrangement of bonds formed with the central metal ion.

To elaborate, the geometry of a metal complex is primarily dictated by the coordination number, which refers to the number of ligand atoms that are directly bonded to the central metal ion. This coordination number is affected by the nature of the ligands involved. For instance, monodentate ligands, such as water ($\text{H}_2\text{O}$) or ammonia ($\text{NH}_3$), can form only a single bond with the central metal ion. As a result, they often lead to geometries such as tetrahedral or octahedral. In contrast, bidentate ligands, such as ethylenediamine ($\text{C}_2\text{H}_8\text{N}_2$), can form two bonds with the central metal ion, frequently resulting in square planar or octahedral geometries.

The geometry is also influenced by the ‘chelate effect,’ which pertains to the stability of chelating ligands. Chelating ligands can form multiple bonds with the central metal ion, leading to more stable complexes. This enhanced stability arises from an increase in entropy during the formation of a chelate complex, as one metal ion effectively replaces several individual ligands. Consequently, this stabilization results in a more probable and stable geometry.

Moreover, the electronic properties of the ligands can impact the geometry of the complex as well. Certain ligands, known as $\pi$-donors, can donate electron density into the d-orbitals of the metal ion, thus stabilizing particular geometries. On the other hand, $\pi$-acceptor ligands can accept electron density from the metal ion, promoting the stabilization of different geometries. For example, carbon monoxide ($\text{CO}$) is a strong $\pi$-acceptor ligand and tends to form complexes characterized by a linear geometry.

Finally, the size and shape of the ligand play an essential role in determining the geometry of the complex. Larger ligands may introduce steric hindrance, which can obstruct the formation of certain geometries. For instance, a bulky ligand may inhibit the formation of a square planar complex, as there may not be adequate space around the metal ion to accommodate four large ligands. Instead, such a situation could favor the formation of tetrahedral or octahedral complexes.

In summary, the type of ligand influences the geometry of a metal complex through various factors, including the coordination number, the chelate effect, electronic properties, and steric hindrance.