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Mathematics
Mathematics
Problem
In
△
D
E
F
\triangle DEF
△
D
E
F
,
∠
D
=
∠
E
\angle D = \angle E
∠
D
=
∠
E
. The internal angle bisector of
∠
D
\angle D
∠
D
meets side
E
F
EF
E
F
at
G
G
G
, and the internal angle bisector of
∠
E
\angle E
∠
E
meets side
D
F
DF
D
F
at
H
H
H
. (a) Prove that
△
D
G
H
≅
△
E
H
G
\triangle DGH \cong \triangle EHG
△
D
G
H
≅
△
E
H
G
. (b) Deduce that
D
G
=
E
H
DG = EH
D
G
=
E
H
. (c) Show that
G
H
GH
G
H
is parallel to
D
E
DE
D
E
.
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