Final answer:
CPCTC cannot be used to initially prove triangles congruent; it is applied after triangles have been proven congruent using one of the congruence postulates or theorems. CPCTC allows for the assertion that corresponding sides and angles of congruent triangles are also congruent.
Step-by-step explanation:
Corresponding Parts of Congruent Triangles are Congruent (CPCTC) is a powerful tool in geometry for proving that specific parts of one triangle are congruent to corresponding parts of another triangle. However, it is important to note that CPCTC cannot be used to prove triangles congruent; rather, it is used after triangles have been proven congruent, using congruence postulates or theorems such as Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), or Hypotenuse-Leg (HL) for right triangles.
Once two triangles are shown to be congruent, CPCTC can be employed to assert that corresponding sides and angles are also congruent. For example, if two triangles are proven congruent by the SSS congruence postulate, then CPCTC justifies that all corresponding angles are congruent.
The principles of geometry used to prove triangle congruence are analogous to other scientific and mathematical concepts.
For example, the Pythagorean theorem is a fundamental principle in mathematics that describes the relation of the sides of a right triangle. Similar to the logical flow of postulates and theorems in geometry, physics also follows a set of postulates to describe nature, and these theories can be experimentally verified to ensure their validity.