Question

in the given figure AM is the median of triangle ABC such that angle AMB = angle AMC.Which of the following is not always true

Answer 1

option (4) is not always true

Answer 2

$AM \: is \: median \:of \: \triangle ABC ,\\such \:that \: \angle {AMB} = \: \angle {AMC}$

$In \:\triangle {AMB} \:and \: \triangle {AMC}$

$BM = MC \: ( AM \: is \: median )$

$\angle {AMB} = \: \angle {AMC}\: (given)$

$AM = AM \: ( common \:side )$

$\therefore \triangle {AMB} \cong \: \triangle {AMC}$

$\blue { ( S.A.S \: Congruence \:rule ) }$

$AB = AC \: ( CPCT )$

$\angle {ABC } = \angle {ACB}$

$\angle {BAC} = 90\degree \: \red{ ( not \: always \:true ) }$

$\angle {BAM } = \angle {CAM} \: ( CPCT)$

Therefore.,

$Option \: \pink { ( 3 ) } \: is \: not \: always \:true$

•••♪