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P,Q and R are the midpoints of AO,BO and CO respectively as shown in figure.Prove that trangle ABC and triangle PQR are equiangular



P is the midpoint of OA and Q is the midpoint of OB
By midpoint theorem,
⇒∠OPQ=∠OAB(alt. opp angles)⇒1


By adding  equations 1& 2 we get
Similarly by adding 3&4 and 5&6 we get ∠C=∠R and∠B=∠Q respectively
Therefore ΔABC and ΔPQR are equiangular
Hence proved

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