Question

How can we prove that all the angle of rhombus are equal and bisect each other at right angle?​

Answer 1

Answer:by using similarity concept

Step-by-step explanation:

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.