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Standard IX
Mathematics
SAS Criteria for Congruency
Question
In the given figure,
O
A
=
O
B
,
O
C
=
O
D
,
∠
A
O
B
=
∠
C
O
D
.
Which of the following statements is true
?
A
C
=
C
D
O
A
=
O
D
A
C
=
B
D
∠
O
C
A
=
∠
O
D
C
A
O
A
=
O
D
B
A
C
=
B
D
C
∠
O
C
A
=
∠
O
D
C
D
A
C
=
C
D
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Solution
Verified by Toppr
The correct option is
C
A
C
=
B
D
In
△
s
A
O
C
and
B
O
D
O
A
=
O
B
(Given)
O
C
=
O
D
(Given)
∠
A
O
B
−
∠
C
O
B
=
∠
C
O
D
−
∠
C
O
B
,
i.e.,
∠
A
O
C
=
∠
B
O
D
∴
△
A
O
C
≅
△
B
O
D
(SAS)
⇒
A
C
=
B
D
(cpct)
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2
Similar Questions
Q1
O
A
=
O
B
,
O
C
=
O
D
,
∠
A
O
B
=
∠
C
O
D
. Prove that
A
C
=
B
D
View Solution
Q2
In the given figure,
O
A
=
O
B
,
O
C
=
O
D
,
∠
A
O
B
=
∠
C
O
D
.
Which of the following statements is true
?
View Solution
Q3
Check whether the following statement is true or not:
Let the line segment AB and CD intersect at O in such a way that OA=OD and OB=OC then AC=BD, but AC may not be parallel to BD.
View Solution
Q4
OA perpendicular to OD, OC perpendicular to OB, OD = OA, OC = OB. Then prove that AB = CD
View Solution
Q5
In trapezium
A
B
C
D
, side
A
B
∥
C
D
and diagonals
A
C
and
B
D
intersect each other at
O
.
Prove that:
O
A
O
C
=
O
D
O
B
.
View Solution