question_answer

In \[\Delta PQR,\text{ }PS\bot QR,\text{ }\angle Q=\angle R\]. State by which property \[\Delta PSQ=\cong \Delta PSR\]?

A)  SAS property                  

B)  ASA property

C)  RHS property                 

D)  All i.e. (a), (b) and (c)

Correct Answer: D

Solution :

(d): In two \[\Delta les,\]if two corresponding \[\angle les\] are equal, then the remaining  third (corresponding) \[\angle les\] are also equal. \[\therefore \,\,\,\angle QPS=\angle RPS\]                         Thus, in Ales PSQ and PSR,   PS (common side) : \[\,\angle PSQ=\angle PSR=90{}^\circ ,\] \[\,\angle QPS=\angle RPS\] By pytharos theorem, All three properties - ASA, SAS and RHS apply.