Question

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

Answer 1

Step-by-step explanation:

ABCD is rhombus

AB = AD

also diagonals bisect each other

DO = OB

AO is common

so

Triangle AOD congruent to triangle AOB

so angle AOD = angle AOB.c.p.c.t.

but angle AOD + angle AOB = 180..linear pair

so angle AOD = angle AOB = 90

Answer 2

Answer :

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

o

[ Linear pair ]

⇒ 2∠AOD=180

o

.

∴ ∠AOD=90

o

.

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

Hope its helpful