The required congruency rule to prove △PQS≅△RQS is SAS congruency rule. Option B is correct.
Given:
The value of x is 6.
It is required to prove that △PQS≅△RQS.
Now, put the value of x=6 in the dimensions shown in the given figure:
[tex]PQ=3x+1\\PQ=19\\RQ=2x+7\\RQ=19\\\angle PQS=(x+3)^{\circ}\\=9^{\circ}\\\angle RQS=(2x)^{\circ}\\=9^{\circ}[/tex]
From the above values, it can be concluded in triangle PQS and RQS that,
[tex]PQ=RQ\\\angle PQS=\angle RQS\\SQ=SQ[/tex]
So, by using SAS congruency rule, △PQS≅△RQS.
Therefore, the required congruency rule to prove △PQS≅△RQS is SAS congruency rule. Option B is correct.
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https://brainly.com/question/19883734
