Question

In a quadrilateral PQSR, with a diagonal PS, if $QS=SR$ and $\angle QSP=\angle RSP$, then consider the following statements
Assertion (A) : $\angle QPS=\angle RPS$
Reason (R) : Triangles QPS and RPS are congruent.Of these statements

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is not a correct explanation of A
• C. A is true, but R is false
• D. A is false, but R is true

Answer 1

The correct option is A Both A and R are true and R is the correct explanation of A

In $△QPS$ and $△RPS$,

$\Rightarrow$ $QS=SR$ [ Given ]

$\Rightarrow$ $QSP=\angle RSP$ [ Given ]

$\Rightarrow$ $SP=PS$ [ Common side ]

$\Rightarrow$ $△QPS\cong △RPS$ [ By SAS Congruence rule ]

$\Rightarrow$ $\angle QPS=\angle RPS$ [ CPCT ]

$\therefore$ Both assertion and reason are correct and reason is correct explanation of assertion.