Show that each diagonal of a rhombus bisects the angle through which it passes. Let ABCD be a rhombus whose diagonal AC and BD intersect each other at O.
In `triangle AOD and triangle AOB`
`AD=AB`(sides of rhombus are equal)
`AO=AO`(common side)
`DO=OB`(diagonals bisect each other)
`triangle AOD cong triangle AOB`
`angleDAO=angle BAO`(cpct)
`angle ABO=angle CBO `
`angleADO =angle CDO `
Hence proved

Explanation

Let ABCD be a rhombus whose diagonal AC and BD intersect each other at O.
In `triangle AOD and triangle AOB`
`AD=AB`(sides of rhombus are equal)
`AO=AO`(common side)
`DO=OB`(diagonals bisect each other)
`triangle AOD cong triangle AOB`
`angle DAO=angle BAO`(cpct)
`angle ABO=angle CBO `
`angle ADO =angle CDO `
Hence proved.