Question

Diagonals AC and BD of a trapezium ABCD with AB||DC intersect each other at O. Prove that diagonals of a rectangle is equal​

Answer 1

Using Theorem:-

Two Triangles on the same base and between

the same parallels are equal in area.

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Given:-

Diagonals AC and BD of a trapezium ABCD

with AB || DC intersect each other at O. 

 

To Prove:-

ar (AOD) = ar (BOC).

Proof:-

Here, △DAC and △DBC lie on the same base DC and between thesame parallels AB and CD.

∴ ar(△DAC) = ar(△DBC)

 ar(△DAC) − ar(△DOC) = ar(△DBC) − ar(△DOC)

 

[On subtracting ar(△DOC) from both sides]

ar(△AOD) = ar(△BOC)

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Hope this will help you...!!

Answer 2

GIVEN THAT

• ABCD is a trapezium with AB || DC
• 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.

HOPE this helps you ☺️