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
property. so, \\( \overline { ac } \cong \overline { 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 the transitive property

The transitive property states that if \(a = b\) and \(b = c\), then \(a = c\).
In this case, we have \(CB=6\) and \(6 = AC\).

Step2: Apply the transitive property

By the transitive property, since \(CB = 6\) and \(6=AC\), we can conclude that \(AC = CB\).

Answer:

transitive