Question

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 definitio segments.
finally, c is the midpoint of a divides ab into
two congruent segments.

Explanation:

Step1: Recall the transitive property

The transitive property states that if \(a = b\) and \(b = c\), then \(a = c\).

Step2: Apply the transitive property

We know that \(CB=6\) and \(6 = AC\). By the transitive property of equality (if \(CB = 6\) and \(6=AC\), then \(AC = CB\)).

Answer:

transitive