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Standard X
Mathematics
Question
The given figure shows a trapezium
A
B
C
D
in which
A
B
is parallel to
D
C
and
A
D
=
B
C
.
Prove that :
O
A
=
O
B
and
O
C
=
O
D
Open in App
Solution
Verified by Toppr
Draw
D
M
⊥
A
B
and
C
N
⊥
A
B
Δ
D
A
M
≡
Δ
C
B
N
by R.H.S.
∴
∠
D
A
B
=
∠
C
B
A
⇒
∠
A
D
C
=
∠
B
C
D
(Supplements of equal angles
D
A
B
and
C
B
A
).
Now by SAS,
Δ
A
D
B
≡
Δ
A
D
B
Further,
Δ
O
A
D
≡
Δ
O
B
C
...... By ASA
⇒
O
A
=
O
B
and
O
C
=
O
D
[C.S.C.T.]
[
h
e
n
c
e
p
r
o
v
e
d
]
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