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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
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
and state the congruence criterion used. b. (ii) Show that
∠
A
D
B
=
∠
A
D
C
\angle ADB = \angle ADC
∠
A
D
B
=
∠
A
D
C
. c. (iii) Hence, prove that
A
D
⊥
B
C
AD \perp BC
A
D
⊥
B
C
.
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