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When all four sides of a quadrilateral are equal, then it is either a square or a rhombus.
Now, in both cases, the diagonals are perpendicular bisector of each other.
Again from the figure,
∠AOB = ∠BOC = ∠COD = ∠AOD = 90
and AB = BC = CD = DA
Now, from triangle AOB and BOC,
AO = OC
OB = OB {common}
AB = CD {given}
So, from SSS congruency,
ΔAOB ≅ ΔBOC
Now, in both cases, the diagonals are perpendicular bisector of each other.
Again from the figure,
∠AOB = ∠BOC = ∠COD = ∠AOD = 90
and AB = BC = CD = DA
Now, from triangle AOB and BOC,
AO = OC
OB = OB {common}
AB = CD {given}
So, from SSS congruency,
ΔAOB ≅ ΔBOC
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