In fig $A B = C F, E F = B D$ and $A F E = ∠ C B D$ prove that
$△ A F E = △ C B D$
$A E = C D$

Open in App

Solution

In $Δ A F E$
$A F = A C - C F = A C - A B - - - - - (1)$ [ $A B = C F$ is given]
In $Δ C B D$
$C B = C A - B A - - - - - (2)$
From $(1)$ and $(2)$
$A F = C B - - - - I$
Now in $Δ A F E$ and $Δ C B D$
$, E F = D B$ [Given} $A F E = ∠ C B D$ [Given]
$A F = C B$ [From $I$ ]
$∴ Δ A F E ≅ Δ C B D$
Thus Corresponding side of these triangles are equal
$∴ A E = C D$

Suggest Corrections

Similar questions

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

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.
Is $△ A F E ≅ △ C B D$ ? If yes, then by which criterion?

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

Join BYJU'S Learning Program