Question

Prove that if the diagonals of a quadrilateral divide each other proportionally

Answer 1

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)

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Therefore, DC∣∣AB

Hence, ABCD is a trapezium.

solution