PQR is a triangle and PS bisects angle QPR show that (a)PQ>QS (b)PR>RS (c)(PQ+PR)>QR

 

Asked by sonalagarwalagarwal544 | 3rd Jun, 2021, 08:34: AM

Expert Answer:

begin mathsize 14px style angle end style PSQ = sum of interior angles of Δ PQR  = begin mathsize 14px style angle end stylePRS + begin mathsize 14px style angle end styleRPS  .........................(1)
Since PS bisects begin mathsize 14px style angle end styleQPR , we have begin mathsize 14px style angle end styleQPS = begin mathsize 14px style angle end styleRPS  .......................(2)
From eqn.(1) and (2)  begin mathsize 14px style angle end stylePSQ = begin mathsize 14px style angle end stylePRS + begin mathsize 14px style angle end styleQPS
Hence begin mathsize 14px style angle end stylePSQ > begin mathsize 14px style angle end styleQPS  ,  Hence in Δ PQS , we get PQ > QS  ...................(3)
In similar way , we can get PR > RS  ...................... (4)
 
By adding eqn.(3) and (4) , we get , ( PQ + PR ) > (QS + RS ) 
 
we get , ( PQ + PR ) > QS

Answered by Thiyagarajan K | 20th Sep, 2021, 02:04: PM