In the given figure, AB = CF, EF = BD, and $∠$ AFE = $∠$ DBC.
Is $△ A F E ≅ △ C B D$ ? If yes, then by which criterion?

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Solution

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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Similar questions

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

In the given figure, AB = CF, EF = BD and $∠$ AFE = $∠$ DBC. Then $△$ AFE is congruent to $△$ CBD by which criterion?

A B = C F, E F = B D

A F E = ∠ C B D

△ A F E = △ C B D

∠ A F E = ∠ D B C

Δ A F E = Δ C B D

A B = C F, E F = B D

A F E = ∠ C B D

△ A F E = △ C B D

A E = C D