Given: ab = 12 ac = 6 prove: c is the midpoint of 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 property. so, ac ≅ cb by the definition of congruent segments. finally, c is the midpoint of ab because it divides ab into two congruent segments.