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In Triangle ADB and Triangle ADC
Angle BAD = Angle CAD (given)
AB = AC (given)
AD = AD (Common)
Hence triangle ADB ≅ ADC (SAS)
Angle B = Ancle C (C.P.C.T)
BD = DC (C.P.C.T)
Angle BDA = Angle CDA
Angle bda + angle cda = 180
2 Angle Bda = 180
Angle BDA = 90
Both angles will be 90, hence it is perpendicular.
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In ABD and ACD
AD=AD common
AB=AC given
BAD=CAD given
therefore ABD=~ACD
hence B= C cpct
and ADB=ADC cpct
but BC is a straight line
so ADB+ADC=180°
2 ADC =180°
ADC =90° =ADB
hence AD is perpendicular to BC
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