The tendency of solid to maintains shape against any external force is rigidity while the property of gas when applying high pressure the volume of gas decreases is compressibility

Rigidity:
Rigidity refers to the resistance of a material to deformation or bending. It is the ability of a material to maintain its shape when subjected to external forces. A rigid material does not easily bend or flex when pressure is applied to it. This property is important in structural engineering, where rigidity ensures that a structure can support its own weight and any additional loads placed on it without collapsing or deforming.

Compressibility:
Compressibility is the ability of a material to decrease in volume when subjected to pressure. It is a measure of how much a material can be compressed or squeezed together. Compressibility is important in various applications, such as in hydraulic systems where fluids need to be compressed to transmit force or in the design of shock-absorbing materials that can absorb impact energy by compressing.

Comparison:
While rigidity and compressibility may seem like opposite properties, they are actually interconnected. In general, rigid materials are less compressible, as they are less likely to change shape or volume when pressure is applied. On the other hand, more compressible materials tend to be less rigid and can deform more easily under pressure.

Conclusion:
Understanding the concepts of rigidity and compressibility is crucial in various fields, from civil engineering to materials science. By knowing how materials behave under different conditions, engineers and designers can choose the right materials for the intended application, ensuring the safety and efficiency of structures and products.