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RHS Criteria for Congruency

In the given ...

Question

In the given figure it is given that AB = CF, EF = BD and $∠$ AFE = $∠$ DBC. Then by which criterion $△ A F E ≅ △ C B D$ ?

A

SAS

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B

SSS

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C

ASA

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D

None of these

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Solution

The correct option is A
SAS

In the given figure,

AB = CF

AB + BF = CF + BF
[Adding BF on both the sides]

AF = CB

In $△ A F E$ and $△ C B D$

AF = CB [Proved above]

EF = BD [Given]

$∠ A F E = ∠ D B C$ [Given]

$∴ △ A F E ≅ △ C B D$ [SAS criterion]

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