Question

prove that the diagonals of a rhombus bisect each other at right angle​

Answer 1

Hey Mate!!

Let ABCD is a rhombus.

⇒ AB=BC=CD=DA [ Adjacent sides are equal in rhombus ]

In △AOD and △COD

⇒ OA=OC [ Diagonals of rhombus bisect each other ]

⇒ OD=OD [ Common side ]

⇒ AD=CD [ Already given ]

∴ △AOD≅△COD [ By SSS congruence rule ]

⇒ ∠AOD=∠COD [ CPCT ]

⇒ ∠AOD+∠COD=180° [ Linear pair ]

⇒ 2∠AOD=180°

∴ ∠AOD=90°

Hence, the diagonals of a rhombus bisect each other at right angle.

Hope this helps you!!

Answer 2

★ Proof:

Let ABCD is a rhombus.

⇒  AB=BC=CD=DA ______ [ Adjacent sides are eqaul in rhombus ]

In △AOD and △COD

⇒  OA=OC ______[ Diagonals of rhombus bisect each other ]

⇒  OD=OD ________[ Common side ]

⇒  AD=CD         

∴  △AOD≅△COD  ______[ By SSS congruence rule ]

⇒  ∠AOD=∠COD________ [ CPCT ]

⇒  ∠AOD+∠COD=180° ______[ Linear pair ]

⇒  2∠AOD=180°

∴  ∠AOD=90°

Hence, the diagonals of a rhombus bisect each other at right angle.

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