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Mathematics
Problem
In
△
A
B
C
\triangle ABC
△
A
B
C
,
A
D
AD
A
D
is a median to side
B
C
BC
B
C
. It is given that
∠
B
A
D
=
∠
C
A
D
\angle BAD = \angle CAD
∠
B
A
D
=
∠
C
A
D
. a. (i) Prove that
A
B
=
A
C
AB = AC
A
B
=
A
C
. b. (ii) Using the result of part (i), show that
∠
A
B
D
=
∠
A
C
D
\angle ABD = \angle ACD
∠
A
B
D
=
∠
A
C
D
. c. (iii) Hence, prove that
A
D
⊥
B
C
AD \perp BC
A
D
⊥
B
C
.
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