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Mathematics
Mathematics
Problem
In
△
A
B
C
\triangle ABC
△
A
B
C
, it is given that
A
B
=
A
C
AB = AC
A
B
=
A
C
. The bisector of
∠
A
\angle A
∠
A
meets
B
C
BC
B
C
at
D
D
D
. (i) Prove that
△
A
B
D
≅
△
C
A
D
\triangle ABD \cong \triangle CAD
△
A
B
D
≅
△
C
A
D
. (ii) Deduce that
B
D
=
D
C
BD = DC
B
D
=
D
C
. (iii) Is
A
D
AD
A
D
perpendicular to
B
C
BC
B
C
? Give a reason for your answer.
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