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 congruent segments. finally, ( c ) is the mid - point because it divides ( overline{ab} ) into two congruent segments. congruence symmetric reflexive transitive

Explanation:

Step1: Recall the transitive property

If \(a = b\) and \(b = c\), then \(a = c\).

Step2: Apply to the problem

Here \(CB=6\), \(6 = AC\), so \(AC = CB\) (by transitive property as \(CB\) and \(AC\) are both equal to \(6\)).

Answer:

transitive