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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
. The line segment
A
D
AD
A
D
is drawn perpendicular to
B
C
BC
B
C
with
D
D
D
lying on
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
B
D
=
D
C
BD = DC
B
D
=
D
C
. c. (iii) Further, prove that
∠
A
B
D
=
∠
C
A
D
\angle ABD = \angle CAD
∠
A
B
D
=
∠
C
A
D
.
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