In figure, if $A B = A C$ and $A P = A Q$ , then by which congruence criterion $Δ P B C ≅ Δ Q C B$ ?

S S S

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A S A

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S A S

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R H S

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Solution

The correct option is C $S A S$
In the given triangle:
$A B = A C$
$\Rightarrow ∠ B = ∠ C$ (As angles opposite to equal to opposite sides are equal.
$A B = A C$
$A P + P B = A Q + Q C$
Now $A P = A Q$
$\Rightarrow P B = Q C$
Now in $△ P B C$ and $△ Q C B$
$P B = Q C$ (Proved above)
$∠ B = ∠ C$ (Proved above)
$B C = C B$ (Common side)
$∴ △ P B C ≅ △ Q C B$ by $S A S$ criteria.

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