Question
If $\triangle\text{PQR }$ and $\triangle\text{SQR}$ are both isosceles triangle on a common base $QR$ such that $P$ and $S$ lie on the same side of $QR.$ Are triangles $PSQ$ and $PSR$ congruent? Which condition do you use$?$
✓
Answer
In $\triangle\text{PSQ}$ and $\triangle\text{PSR},$
$PQ = PR [$given$]$
$SQ = SR [$given$]$
$PS = PS [$common side$]$
By $SSS$ congruence criterion, $\triangle\text{PSQ}\cong\triangle\text{PSR}$
$PQ = PR [$given$]$
$SQ = SR [$given$]$
$PS = PS [$common side$]$
By $SSS$ congruence criterion, $\triangle\text{PSQ}\cong\triangle\text{PSR}$
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