Question

Arrange the reasons for the proof in the correct order. Prove: If the diameter of a circle is 6 meters and the formula for diameter is d = 2r, then the radius of the circle is 3 meters.

Answer 1

Given the question: Arrange the reasons for the proof in the correct order. Prove: If the diameter of a circle is 6 meters and the formula for diameter is d = 2r, then the radius of the circle is 3 meters.
A. If r ≠ 3 m, then d ≠ 6 m. Since the contrapositive is true, the original statement must also be true. Therefore, if the diameter of a circle is 6 meters, then the radius is 3 meters.
B. Multiplication of real numbers shows that d = 2(2 m) = 4 m.
C. Substitute r = 2 m into d = 2r.
D. Assume that r ≠ 3 m. For example, the radius equals another length, such as r = 2 m.

To prove that if the diameter of a circle is 6 meters and the formula for diameter is d = 2r, then the radius of the circle is 3 meters by contradiction, we assume that the radius in not equal to 3 meters, for example, the radius equals another length, such as r = 2 m.
Next, we substitute the value: r = 2m nto the original equation that says that d = 2r, i.e. d = 2(2m) = 4m which is not true and contradicts the original statement that the diameter of the circle is 6m.

Therefore, the arrangement of the proof is as follows:
 D. Assume that r ≠ 3 m. For example, the radius equals another length, such as r = 2 m.
C. Substitute r = 2 m into d = 2r.
B. Multiplication of real numbers shows that d = 2(2 m) = 4 m.
A. If r ≠ 3 m, then d ≠ 6 m. Since the contrapositive is true, the original statement must also be true. Therefore, if the diameter of a circle is 6 meters, then the radius is 3 meters.

D C B A.