Question

given: ab = 12
ac = 6
prove: c is the midpoint of (overline{ab}).
diagram: a---c---b
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 blank 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: Identify the property

We know that \( CB = 6 \) and \( AC = 6 \). The property that states if \( a = b \) and \( b = c \), then \( a = c \) is the transitive property of equality. Here, since \( CB = 6 \) and \( 6 = AC \), by the transitive property, \( AC = CB \).

Answer:

transitive (of equality)