Question: Let P, Q, R be points on a common line with Q separating P and R. Let P', Q', R' be points on another

Let P, Q, R be points on a common line with Q

Let P, Q, R be points on a common line with Q separating P and R. Let P', Q', R' be points on another common line with Q' separating P' and R'. Assume that |PQ| = |P'Q'| and |QR| = |Q'R'|. Prove that the centres of the line segments PP', QQ', and RR' 1lie on a common line. Hint: prove that there is an isometry reversing orientation mapping P, Q, R to P', Q', R'.

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