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  • In Fig, PR > PQ and PS bisects ∠ QPR. Prove that ∠ PSR > ∠ PSQ.

5.  In Fig ,  \small PR>PQ  and PS bisects \small \angle QPR. Prove that  \small \angle PSR>\angle PSQ.

  

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We are given that \small PR>PQ.

Thus  \angle PQR\ =\ \angle PRQ

Also,  PS bisects \small \angle QPR , thus :

  \angle QPS\ =\ \angle RPS

Now, consider \Delta QPS, 

  \angle PSR\ =\ \angle PQR\ +\ \angle QPS                (Exterior angle)

Now, consider \Delta PSR, 

  \angle PSQ\ =\ \angle PRQ\ +\ \angle RPS

Thus from the above the result we can conclude that :

 \small \angle PSR>\angle PSQ

Posted by

Sanket Gandhi

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