Question

One side and one diagonal of a rhombus are given. Then which of following property will be helpful to construct it * a) diagonals bisect each other b) all sides of rhombus are equal c) diagonals bisect at right angles​

Answer 1

Step-by-step explanation:

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=180o             [ Linear pair ]

⇒  2∠AOD=180o.

∴  ∠AOD=90o.

Answer 2

Answer:

⇒ 2∠AOD=180°

∴ ∠AOD=90°

.

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