If FA = DA and line AE is an angle bisector of angle A, then
$△ A E F ≅ △ A E D$ by criteria.

SAS

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RHS

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Solution

The correct option is A SAS
Given, line AE bisects angle A
Therefore, $∠ F A E = ∠ D A E$
In $△ A E F and △ A E D$
1) FA = DA ..... (Given)
2) $∠ F A E = ∠ D A E$ .... (AE is the angle bisector)
3) AE = AE .... (Common side)
So, by SAS criteria for congruency of triangles, $△ A E F ≅ △ A E D$ .

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