Final answer:
The question seems to mix geometry and physics, but lacks clarity and context to provide a precise answer. To prove the isosceles nature of a triangle in geometry, equal angles or sides are demonstrated. For pressure and height relationships in physics, principles of hydrostatics are typically applied.
Step-by-step explanation:
The question appears to involve aspects of geometry and physics, without specific diagrams or a full context it's challenging to give a precise answer. In geometry, to prove that ∆OGK is isosceles, one would typically need to establish that two of its sides are of equal length. This could follow from demonstrating that two of the angles in ∆OGK are equal, which would imply that the sides opposite those angles are also equal. However, given that we do not have a clear description of how points O, G, and K relate to the rectangle PHJM and the lines mentioned, it is not possible to proceed confidently with a proof. For physics-related statements involving pressures P1 and P2, heights h1 and h2, and the gravitational force, one typically applies the principles of hydrostatics to relate the pressure difference to the height difference in a fluid column. The change in pressure is directly proportional to the height difference and the density of the fluid. Without a more specific context or full description of the problem, providing a step-by-step solution isn't feasible. For the third physics concept discussing the changes in heights being proportional to the original heights, it implies a linear relationship between the change in height and the original height, suggesting a property of similar triangles or another geometric relation in a physical context.