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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
. Let
D
D
D
be the midpoint of side
B
C
BC
B
C
. a. (i) Prove that
△
A
B
D
≅
△
A
C
D
\triangle ABD \cong \triangle ACD
△
A
B
D
≅
△
A
C
D
. b. (ii) Hence, show that
A
D
AD
A
D
is both (a) a perpendicular bisector of
B
C
BC
B
C
and (b) an angle bisector of
∠
A
\angle A
∠
A
. c. (iii) If
∠
B
A
C
=
48
∘
\angle BAC = 48^{\circ}
∠
B
A
C
=
4
8
∘
, calculate
∠
B
A
D
\angle BAD
∠
B
A
D
.
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