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

Explanation

Given: ABCD is a rhombus; AC and BD intersect at E.
To prove: AC⊥BD
In rhombus, ABCD
AC and BD intersect each Other at E (Given)
In `/_\ABE and /_\ADE`
AB=AD (sides of a rhombus)
BE=DE (Diagonals bisect each other)
AE common
`:. /_\ABE=/_\ADE`
`:.AEB+AED` (CPCT)
`/_AEB+/_AED=180^@` (Linear pair)
`=>AEB=AED= 180/2 =90^@`
Hence, AC and BD are perpendicular to each other.