Question

Name or state the postulate, property, definition or theorem that justifies the statement.

If W is the midpoint of $\overline{\text{XV}}$, then $\text{XW}=\frac{1}{2}\text{XV}$.

Short answer

The postulate that justifies the statement is the segment addition and midpoint postulate.

Step-by-step solution

Step 1. State the definition of a midpoint.

A midpoint of a segment divides the segment into two equal parts.

Step 2. State the explanation.

The segment addition postulate:

If B lies on a line between two points A and C, then their intersection is a line.

Then, the distance between the points satisfies the conditionAB + BC.

Midpoint postulate:

If a point is a midpoint of the line segment, then it divides the segment in two equal parts.

Thus, this justifies the statement.

Step 3. State the conclusion.

Therefore, the statement is justified by the segment addition and midpoint postulate.