question_answer 1)

Take any point O in the interior of a triangle PQR. Is                                             (i) \[OP+OQ>PQ?\] (ii) \[OQ+OR>QR?\] (iii) \[OR+OP>RP?\]                

Answer:

(i) Yes! \[\text{OP}+\text{OQ}>\text{PQ}\]                                                                         ? (1) \[\left| \begin{align}   & \text{Sum of the lengths of any two sides of a triangle } \\  & \text{is greater than the length of the third side} \\ \end{align} \right.\]        ? (2) (ii) Yes! \[OQ+OR>QR\] \[\left| \begin{align}   & \text{Sum of the length of any two side of a triangle is} \\  & \text{greater than the length of the third side} \\ \end{align} \right.\]        ? (3) (iii) Yes! \[OR+OP>RP\] \[\left| \begin{align}   & ~\text{Sum of the lengths of any two sides of a triangle is} \\  & \text{greater than the length of the third side} \\ \end{align} \right.\]