Question

In figure, if $AB=AC$ and $AP=AQ$, then by which congruence criterion $\Delta PBC\cong \Delta QCB$?

• A. $ASA$
• B. $SSS$
• C. $SAS$
• D. $RHS$

Answer 1

Answer: (C)

In the given triangle:

$AB=AC$

$\Rightarrow \angle B=\angle C$ (As angles opposite to equal to opposite sides are equal.

$AB=AC$

$AP+PB=AQ+QC$

Now $AP=AQ$

$\Rightarrow PB=QC$

Now in $△PBC$ and $△QCB$

$PB=QC$ (Proved above)

$\angle B=\angle C$ (Proved above)

$BC=CB$ (Common side)

$\therefore △PBC\cong △QCB$ by $SAS$ criteria.