In this video, you can see a rigid body, formed by joining two balls, being thrown across the screen. Tracing the trajectory of either ball shows a complicated path. On the other hand, the trajectory of the CM is the familiar parabolic arc of a projectile motion. What does this tell us? When analysing the translational motion of a rigid body, we should can the entire mass of the body to be concentrated at its CM.
We can also assume that the entire weight of a rigid body acts at its CG. For this toy bird, weights cleverly positioned in the tips of the wings positions the CG of the bird just BELOW its beak. With the CG below the pivot, this bird is basically a pendulum.