Question

prove that the diagonals of a rhombus are perpendicular to each other

Answer 1

A rhombus is a parallelogram with all sides equal.
ABCD is a rhombus,diagonals AC and BD intersect at O. ( draw a diagram as i written here then only u can understand this)
Consider ΔAOB and ΔBOC
OA = OC (diagonals of a parallelogram bisect each other)

OB = OB ( common side to ΔAOB and ΔBOC)
AB = BC (sides of rhombus)

∴ΔAOB = ΔBOC(S. S. S rule)

so
but
∴2
similarly
Hence AC is perpendicular on BD
So ,the diagonals of a rhombus are perpendicular to each other.