Question

Prove that the diagonals of a rhombus
intersect each other at right angle.
​

Answer 1

Step-by-step explanation:

Consider the rhombus ABCD

AB=BC=CD=DA (adjecent sides are equal)

in triangleAOD and triangle COD

OA=OC (diagonals of parallogram bisect each other )

OD is common

AD=CD(PROVED ABOVE)

TRIANGLE AOD congurent to triangleCOD(SSS)

ANGLE AOD = ANGLE COD (CPCT)

ANGLE AOD + ANGLE COD = 180 (L P)

2 ANGLE AOD = 180

ANGLE AOD = 90

HENCE PROVED

Answer 2

Answer:

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