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AAS Criteria for Congruency

In the given ...

Question

In the given figure if BE = CF, then which of these following options is correct?

A

$Δ A B C ≅ Δ A C F$

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B

$Δ A B E ≅ Δ A C F$

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C

$Δ A B E ≅ Δ C A F$

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D

$Δ A B C ≅ Δ A F C$

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Solution

The correct option is B
$Δ A B E ≅ Δ A C F$

In $Δ A B E a n d Δ A C F,$
BE = CF [given]
$∠ C F A = ∠ B E A = 90^{\circ}$
$∠ A$ is common.
Hence, $Δ A B E ≅ Δ A C F$ [by A.A.S. Criterion]

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