Question

Which statement is a theorem? A) Three noncollinear points determine a plane. B) Through any two points there is exactly one line. C) A rectangle is a parallelogram with four right angles. D) If C lies on AB and is between A and B, then AC + CB = AB.

Answer 1

D) If C lies on AB and is between A and B, then AC + CB = AB.

Explanation:

Statements A, B and C are postulates while statement D is a theorem.

A postulate is a statement that is true but cannot be proven, but a theorem is a statement that can be proven.

The statement D is the betweenness theorem for points. It states that If C lies on AB and is between A and B, then AC + CB = AB.

This statement can be proven, so it is a theorem.