Question

Given: AB = 12
AC = 6
Prove: C is the midpoint of AB.

A line has points A, C, B.
Proof:
We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the ?

Answer 1

You use the Transitive Property of Equality.

Reasoning: From AC = 6 (given) you used the symmetric property to get 6 = AC. You also found CB = 6. From CB = 6 and 6 = AC, by the Transitive Property (if a = b and b = c then a = c) we get CB = AC. Since C lies on segment AB and AC = CB, C is the midpoint of AB.