Final answer:
Triangle rigidity refers to the property of a triangle that it cannot be deformed without altering its side lengths or internal angles, ensuring the sum of the angles remains constant at 180 degrees. It relates to the broader concept of rigid bodies that do not deform under external forces.
Step-by-step explanation:
Triangle rigidity is a concept in mathematics pertaining to the properties of triangles. When we think of a triangle, we envision a three-sided figure lying on a plane, where the sum of the interior angles equals 180 degrees. This inherent characteristic means that if you try to alter the shape of a triangle without changing the length of its sides, you will inevitably change the angles, thus changing the triangle's shape. This property is why triangles are used in structures as a means of providing stability; because they maintain their shape unless their sides are physically extended or compressed.
A rigid body model is another concept in physics used for analyzing mechanical systems. It explains that an object will not deform under the action of external forces, assuming it is an ideal rigid body. However, in the real world, the material properties will determine the extent of an object's rigidity. Even though some objects may exhibit elasticity under certain forces, they can be considered rigid for practical purposes in various applications like the bouncing of a ping-pong ball and a tennis ball, or in prosthetic limb design.