​in  triangle PQR is an isoceles with PQ=PR. pq is perpendicular to QS and PR is perpendicular to RS. prove that QS= RS

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Please find below the solution to the asked query:

From given information we form our diagram , As :

Here PQR is a isosceles triangle PQ  = PR , From base angle theorem we get

$\angle$ PQR  =  $\angle$ PRQ                                                                                       --- ( 1 )

And given PQ $\perp$ QS and PR $\perp$ RS  , So

$\angle$ PQS  =  $\angle$ PRS = 90$°$

$\angle$ PQS  =  $\angle$ PRS                                                                                        --- ( 2 )

Now we subtract equation 1 from equation 2 and get

$\angle$ PQS  - $\angle$ PQR =  $\angle$ PRS - $\angle$ PRQ

$\angle$ SQR =  $\angle$ SRQ , From base angle theorem in triangle SQR we get

QS =  RS                                                                                                         ( Hence proved )


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