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)

1 answer

To distinguish between the statements:

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

    • This is a definition of a triangle, not a theorem. It defines what a triangle is.
  • Statement #2: The interior angles of any triangle sum to 180 degrees.

    • This is a theorem in geometry, as it can be proven based on the properties of triangles.
  • Statement #3: \( a + b = b + a \)

    • This is known as the commutative property of addition, which is a mathematical property rather than a theorem.

In conclusion: Statement #2 is the theorem.