if ABCD is a parallelogram and AC and BD bisects at O so prove that ABCD is a rhombus
plzz answer this
Share
if ABCD is a parallelogram and AC and BD bisects at O so prove that ABCD is a rhombus
plzz answer this
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
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.