Question

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

If $\overline{BD}\cong \overline{DC}$, then D is the midpoint of $\overline{BC}$.

Short answer

The Midpoint Theorem 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 $\overline{BD}\cong \overline{DC}$.

Step 2. State the midpoint theorem.

The theorem states that the line segment created by joining the midpoints of the triangle’s two sides is parallel and half the length of the third side of the triangle.

Step 3. State the conclusion.

Considering the given diagram and the statement “if $\overline{BD}\cong \overline{DC}$, then D is the midpoint of $\overline{BC}$”

Therefore, the statement about the diagram is justified by the Midpoint Theorem.