Show that if the diagonals of …
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Posted by Vimal Desai 3 years, 4 months ago
- 2 answers
Yogita Ingle 3 years, 4 months ago
Sol: We have a quadrilateral ABCD such that the diagonals AC and BD bisect each other at right angles at O.
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.
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Preeti Singh 3 years, 4 months ago
0Thank You