Question

prove that diagonals of a rhombus are perpendicular to each other

Answer 1

CONSIDER RHOMBUS ABCD
YOU KNOW THAT AB=BC=CD=AD
NOW IN TRIANGLE AOD AND TRIANGLE COD
OA=OC(DIAGONALS OF A //GM BISECT EACH OTHER)
OD=OD (COMMON)
AD=CD
THEREFORE,TRIANGLE AOD CONGRUENT TO TRIANGLE COD (SSS)
THIS GIVES ANGLE AOD = ANGLE COD (CPCT)
BUT, ANGLE AOD + ANGLE COD = 180 (LINEAR PAIR)
SO, 2 ANGLE AOD=180
OR, ANGLE AOD =90
SO,THE DIAGONALS OF A RHOMBUS ARE PERPENDICULAR TO EACH OTHER 
HENCE , PROVED

Answer 2

this is your answer