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If Q is a point between P and R such that PQ = QR, prove that Q is midpoint of PR.

Given that  PQ = QR

PQ + PQ = QR + PQ (equals are added on both sides) -------(1)
Here QR + PQ coincides with PR.
It is known that things which coincides with one another are equal to one another.
So, PQ + QR = PR  --------(2)
From (1) and (2),
PQ + PQ = PR
2PQ = PR
Ie, Q is the midpoint of PR.


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