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as the all sides of rhombus are equal n all the sides of square r also equal so we can say that all rhombses are squares as in diagonals bisect each other so we can say diagonals of rhombus also bisect each other
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Given, ABCD is a rhombus and its diagonals bisect each other.
To prove, diagonals of a rhombus bisect each other at 90°
In COD and COB
CB = CD ( sides of rhombus )
DO = OB ( diagonals bisect each other )
OC = OC ( common )
.`. COD =~ COB by SSS rule
<COD = <COB ( by cpct )
<COD + <COB = 180° ( Linear pair )
<COB + <COB = 180° ( <COB = <COD )
2<COB = 180°
<COB = 180/2
<COB = 90°
SO, <COD = 90°
hence, the diagonals of rhombus bisect at 90°.
To prove, diagonals of a rhombus bisect each other at 90°
In COD and COB
CB = CD ( sides of rhombus )
DO = OB ( diagonals bisect each other )
OC = OC ( common )
.`. COD =~ COB by SSS rule
<COD = <COB ( by cpct )
<COD + <COB = 180° ( Linear pair )
<COB + <COB = 180° ( <COB = <COD )
2<COB = 180°
<COB = 180/2
<COB = 90°
SO, <COD = 90°
hence, the diagonals of rhombus bisect at 90°.
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