Question

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.​

Answer 1

Answer:

good morning everyone have a great day

Answer 2

Answer:

Diagonals are equal

Diagonals are equalAC=BD 1)

)and the diagonals bisect each other at right angles

)and the diagonals bisect each other at right anglesOA=OC;OB=OD (2)

)and the diagonals bisect each other at right anglesOA=OC;OB=OD (2)∠AOB= ∠BOC= ∠COD= ∠AOD= 90

)and the diagonals bisect each other at right anglesOA=OC;OB=OD (2)∠AOB= ∠BOC= ∠COD= ∠AOD= 90 0

)and the diagonals bisect each other at right anglesOA=OC;OB=OD (2)∠AOB= ∠BOC= ∠COD= ∠AOD= 90 0 3)

)and the diagonals bisect each other at right anglesOA=OC;OB=OD (2)∠AOB= ∠BOC= ∠COD= ∠AOD= 90 0 3)

)and the diagonals bisect each other at right anglesOA=OC;OB=OD (2)∠AOB= ∠BOC= ∠COD= ∠AOD= 90 0 3) Proof:

)and the diagonals bisect each other at right anglesOA=OC;OB=OD (2)∠AOB= ∠BOC= ∠COD= ∠AOD= 90 0 3) Proof:Consider △AOB and △COB

)and the diagonals bisect each other at right anglesOA=OC;OB=OD (2)∠AOB= ∠BOC= ∠COD= ∠AOD= 90 0 3) Proof:Consider △AOB and △COBOA=OC from (2)]

rom (2)]∠AOB= ∠COB

rom (2)]∠AOB= ∠COBOB is the common side

rom (2)]∠AOB= ∠COBOB is the common sideTherefore,

rom (2)]∠AOB= ∠COBOB is the common sideTherefore,△AOB≅ △COB

rom (2)]∠AOB= ∠COBOB is the common sideTherefore,△AOB≅ △COBFrom SAS criteria, AB=CB

rom (2)]∠AOB= ∠COBOB is the common sideTherefore,△AOB≅ △COBFrom SAS criteria, AB=CBSimilarly, we prove

rom (2)]∠AOB= ∠COBOB is the common sideTherefore,△AOB≅ △COBFrom SAS criteria, AB=CBSimilarly, we prove△AOB≅ △DOA, so AB=AD

rom (2)]∠AOB= ∠COBOB is the common sideTherefore,△AOB≅ △COBFrom SAS criteria, AB=CBSimilarly, we prove△AOB≅ △DOA, so AB=AD△BOC≅ △COD, so CB=DC

rom (2)]∠AOB= ∠COBOB is the common sideTherefore,△AOB≅ △COBFrom SAS criteria, AB=CBSimilarly, we prove△AOB≅ △DOA, so AB=AD△BOC≅ △COD, so CB=DCSo, AB=AD=CB=DC

Hence proved