1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard IX
Mathematics
Converse of Theorem 2
Diagonals AC ...
Question
Diagonals AC and BD of a trapezium Abcd with Ab|| DC interest each other at O . Prove that ar ( AoB ) = ar (CoD)
Open in App
Solution
Given that ABCD is a trapezium with AB || DC and Diagonal AC and BD intersect each other at O.
To prove: Area (AOD) = Area (BOC)
Proof: ΔADC and ΔBDC are on the same base DC and between same parallel AB and DC.
∴Area (ΔADC) = Area (ΔBDC) [triangles on the same base and between same parallel are equal in area]
Subtract Area (ΔDOC) from both side
Area (ΔADC) – Area (ΔDOC) = Area (ΔBDC) – Area (ΔDOC)
Area (ΔAOD) = Area (ΔBOC)
Hence proved.
Suggest Corrections
0
Similar questions
Q.
Diagonals
A
C
and
B
D
of a trapezium
A
B
C
D
with
A
B
∥
D
C
intersects each other at
O
. Prove that ar
(
△
A
O
D
)
=
ar
(
△
B
O
C
)
.
Q.
Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(ΔAOD) = ar(ΔBOC).