Question

The diagonals of a quadrilateral divide each other proportionally, prove that it is
a trapezium

Answer 1

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Question :-

If the diagonals of a quadrilateral divide each other proportionally, then prove that the quadrilateral is a trapezium.

To find :-

Prove that ABCD Is a trapezium.

Solution :-

Let ABCD be a quadrilateral as shown in the above figure:

Diagonal AC and BD divide each other proportionately that is,

AO/OC = BO/OD

Therefore, the triangles containing these sides are equiangular that is △AOB and △COD and thus,

∠OAB=∠OCD

∠OBA=∠ODC (Alternate angles)

Therefore, DC || AB

Hence, ABCD is a trapezium.

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Answer 2

Answer:

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Step-by-step explanation:

Let ABCD be a quadrilateral as shown in the above figure:

Diagonal AC and BD divide each other proportionately that is,

OC

AO

=

OD

BO

Therefore, the triangles containing these sides are equiangular that is △AOB and △COD and thus,

∠OAB=∠OCD

∠OBA=∠ODC (Alternate angles)

Therefore, DC∣∣AB

Hence, ABCD is a trapezium