What is a statement proven true using undefined terms

Subject : Social Studies

Question: What is a statement that can be proven true using undefined terms, definitions, and postulates?

Expert Verified Solution:

A statement that can be proven true using undefined terms, definitions, and postulates is called a theorem.

Explanation:

Undefined terms are basic concepts that are not defined using other terms but are understood intuitively, such as “point,” “line,” and “plane” in geometry.

Definitions are formal explanations of terms using undefined terms or other defined terms.

Postulates (or axioms) are statements accepted as true without proof, serving as the foundational building blocks for logical reasoning in mathematics.

A theorem is a statement proven to be true through a logical sequence of arguments using these undefined terms, definitions, and postulates. An example of a theorem is the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This theorem can be proven using the basic concepts and rules of geometry.