Question

write a two - colum proof. given: bc = 6, ac = 12 prove: b is the midpoint of ac statement: 1. bc = 6, ac = 12 reason: given 2. 3. 4. 5. 6.

Explanation:

Step1: Calculate length of AB

Since $AC=AB + BC$ and $AC = 12$, $BC=6$, then $AB=AC - BC$. So $AB=12 - 6=6$.

Step2: Compare AB and BC

We found that $AB = 6$ and $BC = 6$, so $AB=BC$.

Step3: Recall mid - point definition

The mid - point of a line segment divides the line segment into two equal parts.

Step4: State the conclusion

Since $AB = BC$ and $A$, $B$, $C$ are collinear, $B$ is the mid - point of $AC$.

Answer:

Statement	Reason
2. $AB=AC - BC$	Segment addition postulate
3. $AB = 12-6=6$	Substitution property of equality
4. $AB = BC$	Substitution ($AB = 6$, $BC = 6$)
5. The mid - point of a line segment divides it into two equal parts	Definition of mid - point
6. $B$ is the mid - point of $AC$	By 4 and 5