Mathematics
In the given figure, AM is the perpendicular bisector of BC. Then :
AB = AM
AC = BM
AB ≠ AC
AM bisects ∠BAC
Triangles
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Answer
From figure,
In △ ABM and △ ACM,
⇒ ∠AMB = ∠AMC (Both equal to 90°)
⇒ BM = MC (Since, AM is perpendicular bisector of BC)
⇒ AM = AM (Common side)
∴ △ ABM ≅ △ ACM (By S.A.S. axiom)
We know that,
Corresponding parts of congruent triangles are equal.
∴ ∠BAM = ∠CAM (By C.P.C.T.C.)
∴ AM bisects ∠BAC.
Hence, Option 4 is the correct option.
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