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Byju's Answer
Standard IX
Mathematics
Opposite Sides of a Parallelogram Are Equal
ABCD is a qua...
Question
A
B
C
D
is a quadrilateral in which
A
D
=
B
C
and
∠
D
A
B
=
∠
C
B
A
.
Prove that
B
D
=
A
C
.
Open in App
Solution
In
△
A
B
D
and
△
B
A
C
,
A
D
=
B
C
[ Given ]
∠
D
A
B
=
∠
C
B
A
[ Given ]
A
B
=
B
A
[ Common side ]
So, by the Side-Angle-Side criterion of congruence,
△
A
B
D
≅
△
B
A
C
∴
B
D
=
A
C
[CPCT]
Suggest Corrections
1
Similar questions
Q.
ABCD is a quadrilateral in which
A
D
=
B
C
and
∠
D
A
B
=
∠
C
B
A
. Prove that,
(i)
△
A
B
D
≅
△
B
A
C
(ii)
B
D
=
A
C
(iii)
∠
A
B
D
=
∠
B
A
C
Q.
A
B
C
D
is a quadrilateral in which
A
D
=
B
C
and
∠
D
A
B
=
∠
C
B
A
prove that
△
A
B
D
≅
△
B
A
C
Q.
A
B
C
D
is a quadrilateral in which
A
D
=
B
C
and
∠
D
A
B
=
∠
C
B
A
.
Prove that
(i)
Δ
A
B
D
≅
Δ
B
A
C
(ii)
B
D
=
A
C
(iii)
∠
A
B
D
=
∠
B
A
C
Q.
ABCD is a quadrilateral in which
A
D
=
B
C
a
n
d
∠
D
A
B
=
∠
C
B
A
(See the given figure). Prove that
BD = AC
Q.
Question 2 (ii)
ABCD is a quadrilateral in which
A
D
=
B
C
a
n
d
∠
D
A
B
=
∠
C
B
A
(See the given figure). Prove that
BD = AC
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Opposite Sides of a Parallelogram Are Equal
Standard IX Mathematics
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