Distinguish between the following statements. Which statement is a theorem?

Statement #1: All triangles have three sides and three angles.

Statement #2: The interior angles of any triangle sum to 180 degrees.

Statement #3: a+b=b+a

(1 point)
Statement # is a theorem

1 answer

To distinguish between the statements provided:

  • Statement #1: "All triangles have three sides and three angles."

    • This is a definition of a triangle rather than a theorem. It describes the fundamental characteristics of triangles.
  • Statement #2: "The interior angles of any triangle sum to 180 degrees."

    • This is a theorem in geometry. It can be proven through various methods, such as through parallel lines or by using Euclidean geometry.
  • Statement #3: "a + b = b + a"

    • This is an example of the commutative property of addition. While it's a mathematical principle, it's more of a property than a theorem.

Therefore, Statement #2 is a theorem.