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Standard IX
Mathematics
Question
In an isosceles triangle
A
B
C
with
A
B
=
A
C
,
D
and
E
are points on
B
C
such that
B
E
=
C
D
Show that
A
D
=
A
E
Open in App
Solution
Verified by Toppr
Given
A
B
C
is an isosceles triangle with
A
B
=
A
C
D
and
E
are the point on
B
C
such that
B
E
=
C
D
Given
A
B
=
A
C
∴
∠
A
B
D
=
∠
A
C
E
...........(1)
[opposite angle of sides of a triangle]
Given
B
E
=
C
D
Then
B
E
−
D
E
=
C
D
−
D
E
⇒
B
D
=
C
E
.....................(2)
In
Δ
A
B
D
and
Δ
A
C
E
∠
A
B
D
=
∠
A
C
E
[From 1]
B
D
=
C
E
[From 2]
A
B
=
A
C
[Given]
∴
Δ
A
B
D
≅
Δ
A
C
E
by SAS congruency
By CPCT,
A
D
=
A
E
Proved
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