Given: 2pq=pr prove: q is the midpoint of pr

Using definition of midpoint, Q is the mid point of PR.

Step-by-step explanation:

Given 2PQ=PR

And Q lies on the line PR (It should be given in the problem itself else we have to assume it to prove "Q is the midpoint of PR").

Then PR=PQ+QR using segment addition postulate.

Let us plugin PR in given equation.

2PQ=PQ+QR

Subtract PQ from both sides.

2PQ-PQ=PQ+QR-PQ

PQ=QR

Since Q lies on the line PR and PQ=QR, Q is the mid point of PR.

Hence proved.