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Mathematics
Mathematics
Problem
In
△
A
B
C
\triangle ABC
△
A
B
C
,
A
B
=
A
C
AB = AC
A
B
=
A
C
and the ray
A
D
AD
A
D
bisects
∠
A
\angle A
∠
A
, meeting
B
C
BC
B
C
at
D
D
D
. (a) Prove that
△
A
B
D
≅
△
A
C
D
\triangle ABD \cong \triangle ACD
△
A
B
D
≅
△
A
C
D
. (b) Deduce that
B
D
=
D
C
BD = DC
B
D
=
D
C
. (c) Is
A
D
AD
A
D
necessarily perpendicular to
B
C
BC
B
C
? Give a proof or counter-example with reasoning.
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