Which property measures a material's ability to resist forces that attempt to break or deform it?

The property that measures a material's ability to resist forces that attempt to break or deform it is strength. Strength is a critical aspect when considering the performance of materials under various loading conditions. It refers to the maximum amount of stress a material can withstand without failing, which encompasses both deformational characteristics and ultimate load-bearing capabilities.

When a material is exposed to external forces, its molecular structure plays a vital role in its ability to maintain integrity and shape. A material with high strength will resist deformation and fracture effectively, making it suitable for applications where durability and stability under load are crucial.

The other options relate to different material behaviors. Conductivity pertains to the ability of a material to conduct electricity or heat, ductility refers to a material's capability to undergo significant plastic deformation before rupture—essentially how it can stretch and bend without breaking, while toughness denotes a material's ability to absorb energy and plastically deform without fracturing. Each of these properties contributes to the overall performance of materials but does not directly measure the resistance to breaking or deforming like strength does.