Question

given that d is the midpoint of ab and b is the midpoint of ac, which statement must be true? ad = 1/3 ac ab + dc = ac bk = kc ac = 4db

Explanation:

Step1: Use mid - point property for AB

Since D is the mid - point of $\overline{AB}$, we have $AD = DB=\frac{1}{2}AB$.

Step2: Use mid - point property for AC

Since B is the mid - point of $\overline{AC}$, we have $AB = BC=\frac{1}{2}AC$.

Step3: Express AD in terms of AC

Substitute $AB=\frac{1}{2}AC$ into $AD=\frac{1}{2}AB$. Then $AD=\frac{1}{2}\times\frac{1}{2}AC=\frac{1}{4}AC$.

Step4: Analyze $AB + DC$

$DC=DB + BC$. Since $AD = DB$ and $AB = BC$, $AB+DC=AB+(DB + BC)=(AB + BC)+DB=AC + DB
eq AC$.

Step5: Analyze $BK = KC$

There is no information given about point K to suggest $BK = KC$.

Step6: Express AC in terms of DB

Since $AB = 2DB$ and $AC = 2AB$, then $AC=2\times(2DB)=4DB$.

Answer:

$AC = 4DB$