Yes, objects of the same mass but different shapes will fall at the same rate in a vacuum. This is a fundamental principle of physics known as Galileo's Law of Falling Bodies.

Here's why:

* Gravity acts equally on all objects: The force of gravity depends only on the mass of the objects involved (the object falling and the Earth). So, two objects with the same mass will experience the same gravitational force.

* Air resistance is the key difference: In a vacuum, there is no air resistance to slow objects down. Air resistance depends on the shape and surface area of an object. A flat sheet of paper will fall slower than a crumpled ball of paper because the flat sheet has more surface area exposed to the air, creating more drag.

In the real world, air resistance matters: This is why a feather falls much slower than a rock. Even though they might have the same mass, the feather has a larger surface area and catches more air, slowing it down.

Let me know if you'd like to explore the concept of air resistance in more detail!