Question

Take three collinear points P, Q, R in a plane. Join PQ, QR and RP. Is the figure a triangle? If not, why?

Answer 1

Answer :  

Take three collinear points P, Q and R  

There can be three cases  

Case 1 : P is in middle  

Case 2 : Q is in middle  

Case 3 : R is in middle

 

Case 1 :   QP + RP  = QP   ( hence sum of two side not greater than third side) so this can not be triangle  

Case 2 :   PQ + QR  = PR   ( hence sum of two side not greater than third side) so this can not be triangle  

Case 3 :   PR + RQ  = PQ   ( hence sum of two side not greater than third side) so this can not be triangle  

as Points are collinear hence figure is not a triangle

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