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Byju's Answer
Standard X
Mathematics
Similar Triangles
In parallelog...
Question
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP
=
BQ. Show that
Δ
AQB
≅
Δ
CPD.
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Solution
Here,
A
B
C
D
is a parallelogram.
A
B
∥
D
C
and
B
D
is a transversal.
∴
∠
A
B
Q
=
∠
C
D
P
[ Alternate angles ] ---- ( 1 )
In
△
A
Q
B
and
△
C
P
D
,
⇒
A
B
=
C
D
[ Opposite sides of parallelogram are equal ]
⇒
∠
A
B
Q
=
∠
C
D
P
[ From ( 1 ) ]
⇒
B
Q
=
D
P
[ Given ]
∴
△
A
Q
B
≅
△
C
P
D
[ By SAS congruence ]
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Similar questions
Q.
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:
Δ
A
Q
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≅
Δ
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Q.
Question 9 (iii)
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP=BQ (see the given figure) Show that:
Δ
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Q.
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP
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In parallelogram
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C
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, two point
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and
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are taken on diagonal
B
D
such that
D
P
=
B
Q
. Show that
(i)
△
A
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D
≅
△
C
Q
B
(ii)
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P
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B
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(iv)
A
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(v)
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In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP
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