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Standard VIII
Mathematics
Question
In quadrilateral ABCD, BM and DN are drawn perpendiculars to AC such that BM = DN. If BR = 8 cm, then find BD.
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Solution
Verified by Toppr
Given
A
B
C
D
is a quadrilateral in which diagonals
A
C
and
B
D
intersect each other at
P
Also,
D
N
⊥
A
C
and
B
M
⊥
A
C
D
N
=
B
M
In
△
D
N
P
and
△
B
M
P
we have
∠
D
P
N
=
∠
B
P
M
since they are vertically opposite angles.
∠
D
N
P
=
∠
B
M
P
since each are equal to
90
∘
D
N
=
B
M
(given)
⇒
△
D
N
P
≅
△
B
M
P
by AAS postulate.
⇒
D
P
=
B
P
=
8
cms by CPCT
We have
B
D
=
B
P
+
D
P
=
8
+
8
=
16
cms from the diagram.
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