Question

1. given: 2pq = pr

prove: q is the mid - point of (overline{pr})

statements	reasons
2.	2. segment addition postulate
3. 2pq = pq + qr	3.
4. pq = qr	4.
5.	5. definition of midpoint

Explanation:

Step1: State the given

$2PQ = PR$

Step2: Apply segment - addition postulate

$PR=PQ + QR$

Step3: Substitute $PR$

Since $2PQ = PR$ and $PR = PQ+QR$, we have $2PQ=PQ + QR$

Step4: Subtract $PQ$ from both sides

$2PQ - PQ=PQ + QR - PQ$, so $PQ = QR$

Step5: Use mid - point definition

Since $PQ = QR$, $Q$ is the mid - point of $\overline{PR}$

Answer:

1. $2PQ = PR$; Given
2. $PR=PQ + QR$; Segment Addition Postulate
3. $2PQ=PQ + QR$; Substitution (using 1 and 2)
4. $PQ = QR$; Subtraction Property of Equality (subtracted $PQ$ from both sides of 3)
5. $Q$ is the mid - point of $\overline{PR}$; Definition of Midpoint