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Post Test: Foundations of Geometry

Select the correct answer from each drop-down menu.

1. A statement that is assumed to be true without proof is a(n) __________.
2. A statement that is believed to be true but hasn't been proven is a(n) __________.
3. A statement that has been shown to be true by logical reasoning is a(n) __________.



Answer :

GinnyAnswer

Final answer:

Axioms are assumed true, theorems are proven, and conjectures are beliefs awaiting proof.


Explanation:

Axiom: A statement that is assumed to be true without proof. For example, 'the method of constructing a straight line between two points.'

Theorem: A statement that has been shown to be true by valid reasoning. For instance, 'if we start with four lines that form a rectangle, we can draw a new line dividing it into two triangles.'

Conjecture: A statement believed to be true but not proven. It is a hypothesis waiting for validation through proof.


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