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Byju's Answer
Standard IX
Mathematics
AAS Criteria for Congruency
In adjoining ...
Question
In adjoining figure,
A
D
,
B
E
&
C
F
are altitudes of
△
A
B
C
. If
A
D
=
C
F
=
B
E
.
Prove that
A
B
C
is an equilateral triangle.
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Solution
In
Δ
A
D
C
and
Δ
B
E
C
∠
D
=
∠
E
=
90
∘
A
D
=
B
E
(given)
∠
C
=
∠
C
(common)
∴
Δ
A
D
C
≅
Δ
B
E
C
by AAS property.
A
C
=
B
C
(by CPCT) ____ (1)
In
Δ
A
D
B
and
Δ
C
E
B
∠
D
=
∠
F
(
90
∘
)
,
A
D
=
C
F
(given),
∠
B
=
∠
B
(common)
Δ
A
D
B
≅
Δ
C
F
B
by AAS property
A
B
=
C
B
(by CPCT) _____ (2)
A
B
=
B
C
=
C
B
Hence,
Δ
A
B
C
is equilateral.
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