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Byju's Answer
Standard IX
Mathematics
Congruency of Triangles
In the given ...
Question
In the given figure, C is the mid-point of AB. If
∠DCA = ∠ECB and ∠DBC = ∠EAC, prove that DC = EC.
Figure
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Solution
In
∆
E
C
A
and
∆
D
C
B
,
∠
E
A
C
=
∠
D
B
C
given
A
C
=
B
C
C
is
the
mid
point
of
A
B
Now
,
∠
D
C
A
=
∠
E
C
B
⇒
∠
D
C
A
+
∠
D
C
E
=
∠
E
C
B
+
∠
D
C
E
⇒
∠
A
C
E
=
∠
B
C
D
Therefore
,
by
A
S
A
congruency
criteria
,
∆
E
C
A
≅
∆
D
C
B
.
⇒
D
C
=
E
C
C
orresponding
si
d
es
of
congruent
triangles
are
equal
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Q.
In the given figure, C is the midpoint of AB. If
∠DCA = ∠ECB and ∠DBC = ∠EAC, prove that DC = EC.