Which congruency rule is used to prove the construction of an angular bisector.

SSS

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SAS

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ASS

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RHS

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Solution

The correct option is A SSS
Proof for the construction of an angular bisector:

In $△ B D F$ and $△ B E F$
BD = BE (radii of same arc)
DF = EF (Arcs of equal radii)
BF = BF (Common side)
$△ B D F ≅ △ B E F$ [SSS rule]
So $∠ D B F = ∠ E B F$ [CPCT]
Thus BF is the bisector of $∠ A B C$

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