If a point Q lies between two points P and R such that PQ=QR prove that PQ=1/2PR
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APPLICATION OF COSINE RULE;
PR²=PQ²+QR²-2(PQ)(QR)COS(PQR)
Since P,Q,R lie on the same line,with Q between P&R
Therefore;∠PQR=180°
PR²=PQ²+QR²-2(PQ)(QR)cos(180°)
PR²=PQ²+QR²-2(PQ)(QR)(-1)
PR²=PQ²+QR²+2(PQ)(QR)
PR²=(PQ+QR)²
PQ=1/2PR
PR²=PQ²+QR²-2(PQ)(QR)COS(PQR)
Since P,Q,R lie on the same line,with Q between P&R
Therefore;∠PQR=180°
PR²=PQ²+QR²-2(PQ)(QR)cos(180°)
PR²=PQ²+QR²-2(PQ)(QR)(-1)
PR²=PQ²+QR²+2(PQ)(QR)
PR²=(PQ+QR)²
PQ=1/2PR
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