Question

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In a quadrilateral ABCD the point O denotes the intersection of the diagonals. The perimeters of the triangles AOB, BOC, COD and DOA are equal. Prove that ABCD is a rhombus.


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Answer 1

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● Given that,

perimeters of AOB, BOC, COD AND DOA are equal.

● To prove that,

□ ABCD is a rhombus.

● Proof,

Hence, AOB = BOC = COD = DOA

AB = BC = CD = AD (by C.P.C.T)

If all the sides of a quadrilateral is equal then it is said to be a rhombus.

Hence, ABCD is a rhombus.

Hence, it is proved.

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