Question

Which statement is true with respect to the Euclidean approach to geometry?

a) Point, line, and plane are defined terms.
b) Undefined terms are called axioms.
c) Theorems are used to prove axioms.
d) Axioms are used to prove theorems.
e) Theorems are statements accepted without proof.

Answer 1

The true statement with respect to Euclidean geometry is that axioms are used to prove theorems. Undefined terms provide the basic building blocks for the system, while axioms are accepted principles that underpin proofs of more complex propositions called theorems.

Step-by-step explanation:

The statement that is true with respect to the Euclidean approach to geometry is d) Axioms are used to prove theorems.

In Euclidean geometry, point, line, and plane are undefined terms that serve as the foundation of the system. Undefined terms are used to build definitions of other geometric terms. On the other hand, axioms, or postulates, are fundamental principles that are accepted without proof and are considered to be universally true within the system. These axioms are the starting points for logical deductions in geometry, and they are used to prove more complex statements known as theorems.

Theorems are propositions that have been proven to be true based on axioms, definitions, and previously established theorems. Therefore, option e is incorrect because theorems require proof, and option c is incorrect because axioms are not proven by theorems; instead, it is the other way around.