Question

State which definition, postulate, or theorem justifies the statement about the diagram.

If D is the midpoint of $\overline{BC}$, then $BD=\frac{1}{2}BC$.

Short answer

The statement midpoint of a line divides it into equal parts justifies the statement about the diagram.

Step-by-step solution

Step 1. Observe the given diagram.

The diagram constitutes of a triangle ABC and it is given that D is the midpoint of $\overline{BC}$.

Step 2. State the definition of the midpoint of a line.

In geometry, the midpoint means the middle point of a line. The midpoint divides the line into equal parts that is if D is the midpoint of $\overline{BC}$ then$\overline{BD}=\overline{DC}$ and $\overline{BD}+\overline{DC}=\overline{BC}$ .

Step 3. State the conclusion.

Considering the given diagram and the statement “if D is the midpoint of $\overline{BC}$, then $BD=\frac{1}{2}BC$”

Therefore, the statement about the diagram is justified by the statement midpoint of a line divides it into equal parts.