In Figure. PQ = PS and 1= 2. 1. Is ? give reasons. 2. Is Is QR = … - Vidyadip

Question

In Figure. $PQ = PS$ and $\angle1=\angle2. $

Is $\triangle\text{PQR}\cong\triangle\text{PSR}?$ give reasons.
Is Is $\text{QR} =\text{ SR}?$ Give reasons.

✓

Answer

Yes,

In $\triangle\text{PQR}$ and $\triangle\text{PSR},$

$PQ = PS [$given$]$
$\angle1=\angle2 [$given$]$
$PR = PR [$common side$]$

By $SAS$ congruence criterion, $\triangle\text{PQR}\cong\triangle\text{PSR}$

Yes, $QR = SR$

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