1) show that if the diagonal y a quadlo
bisect each othen at Sight angles, then it is a
hombus
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1) show that if the diagonal y a quadlo
bisect each othen at Sight angles, then it is a
hombus
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Answer:
show that the diagonals of a quadrilateral bisect each other at right angles , then it is a rhombus.
Step-by-step explanation:
Sol: We have a quadrilateral ABCD such that the diagonals AC and BD bisect each other at right angles at O.
∴ In ΔAOB and ΔAOD, we have
AO = AO
[Common]
OB = OD
[Given that O in the mid-point of BD]
∠AOB = ∠AOD
[Each = 90°]
ΔAOB ≌ ΔAOD
[SAS criteria]
Their corresponding parts are equal.
AB = AD...(1)Similarly,AB = BC...(2) BC = CD...(3) CD = AD...(4)
∴ From (1), (2), (3) and (4), we have AB = BC CD = DA
Thus, the quadrilateral ABCD is a rhombus.