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Byju's Answer
Standard VII
Mathematics
Properties of Isosceles and Equilateral Triangles
In an isoscel...
Question
In an isosceles triangle
A
B
C
with
A
B
=
A
C
,
B
D
is perpendicular from
B
to side
A
C
.
Prove that
B
D
2
−
C
D
2
=
2
C
D
.
A
D
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Solution
Since
△
A
D
B
is right-angled at
D
,
A
B
2
=
A
D
2
+
B
D
2
⇒
A
C
2
=
A
D
2
+
B
D
2
(
∵
A
B
=
A
C
)
⇒
(
A
D
+
C
D
)
2
=
A
D
2
+
B
D
2
⇒
A
D
2
+
C
D
2
+
2
A
D
.
C
D
=
A
D
2
+
B
D
2
⇒
B
D
2
−
C
D
2
=
2
A
D
.
C
D
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In an isosceles triangle ABC with AB = AC, BD is perpendicular from B to the side AC. Prove that
B
D
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.
A
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Q.
In an isosceles triangle ABC with AB = AC and BD ⊥ AC. Prove that BD
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