Question

given: ab = 12
ac = 6
prove: c is the midpoint of (overline{ab}).
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 dropdown property. so, (overline{ac}congoverline{cb}) by the definition of congruent segments. finally, c is the midpoint of (overline{ab}) because it divides (overline{ab}) into two congruent segments.

Explanation:

Step1: Recall segment - addition property

$AC + CB=AB$

Step2: Substitute given values

Since $AB = 12$ and $AC = 6$, we have $6+CB = 12$.

Step3: Solve for $CB$

Using subtraction property: $CB=12 - 6=6$.

Step4: Use transitive property

We know $CB = 6$ and $AC = 6$, so by transitive property $AC = CB$.

Answer:

Transitive