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Standard IX
Mathematics
SSS Criteria for Congruency
Question
In the following fig. if
A
B
=
A
C
and
B
D
=
D
C
then
∠
A
D
C
=
60
0
120
0
90
0
None
A
60
0
B
90
0
C
None
D
120
0
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Solution
Verified by Toppr
In
△
A
B
D
and
△
A
C
D
A
B
=
A
C
(Given)
B
D
=
D
C
(Given)
A
D
=
A
D
(Common side)
∴
△
A
B
D
≅
A
C
D
by
S
S
S
criteria.
Now corresponding angles of congruent triangles are equal
⇒
∠
A
D
B
=
∠
A
D
C
Now
∠
A
D
B
+
∠
A
D
C
=
180
∘
(Adjacent angles on staraight line)
⇒
∠
A
D
C
+
∠
A
D
C
=
180
∘
⇒
2
∠
A
D
C
=
180
∘
⇒
∠
A
D
C
=
90
∘
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Similar Questions
Q1
In the following fig. if AB = AC and BD = DC then
∠
A
D
C
=
View Solution
Q2
In the given
Δ
A
B
C
, if
A
B
=
A
C
and
B
D
=
D
C
, then
∠
A
D
C
=
___________.
View Solution
Q3
State true or false.
In the adjoining figure, AB = AC and BD = DC.
If
Δ
A
D
B
≅
Δ
A
D
C
then
∠
A
D
B
+
∠
A
D
C
=
90
∘
.
View Solution
Q4
In
△
ABC ( Fig.4.59 ), if
∠
1 =
∠
2, prove that
A
B
A
C
=
B
D
D
C
.
View Solution
Q5
In fig,
A
D
is the angle bisector of
∠
A
. If
B
D
=
4
c
m
,
D
C
=
3
c
m
and
A
B
=
6
c
m
, determine
A
C
.
View Solution