Question

In the figure PS bisects angle P arrange PQ and QS and SR in the descending order of their lengths . giving reasons !!​

Answer 1

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Answer 2

PQ > SR > QS.

To find : Arrangement of PQ, QS and SR in descending order.

Given :

From the figure,

"PS" bisects ∠P.

∠PQS = 60°

∠PRS = 40°

In ΔPQR,

∠P = 180° - (∠PQS + ∠PRS)      

     = 180° - (60° + 40°)

     = 180° - 100°

     = 80°

∠P = 80°.

Where, PS bisects ∠P.

∠RPS = 40°

∠QPS = 40°

In ΔPRS,

∠PSR = 180° - (∠RPS + ∠QPS)

          = 180° - (40° + 40°)

          = 180° - 80°

∠PSR = 100°  

In ΔPQS,

∠PSQ = 180° - (∠QPS + ∠PQS)

         = 180° - (40° + 60°)

         = 180° - 100°

∠PSQ = 80°

∠QPS = 40° ; ∠PSR = 100° ; ∠PSQ = 80°

PQ > SR > QS.  

Hence, PQ > SR > QS.  

To learn more...

1. "Question 5 In the given figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR >∠PSQ.

brainly.in/question/1411256  

2. PS is the bisector of angle QPR of a triangle pqr prove that QS℅SR= PQ℅SR

brainly.in/question/1195651