Question

Solve it right otherwise I will report you​

Answer 1

Let ABCD is a parallelogram and diagonal ACbisects the angle A.

∴  ∠CAB=∠CAD

AB∥CD and AC is a trasnversal.

∴  ∠CAB=∠ACD          [ Alternate interior angles ]

Again, AD∥BC and AC is a transversal.

∴  ∠CAD=∠ACB        [ Alternate interior angles ]

⇒  So, ∠ACD=∠ACB      [ Since, ∠CAB=∠CAD ]        ---- ( 2 )

⇒  ∠A=∠C                [ Opposite angels of parallelogram are equal ]

⇒  21∠A=21∠C            [ Dividing both sides by 2 ]

⇒  ∠DAC=∠DCA            [ From ( 1 ) and ( 2 ) ]

⇒  CD=AD          [ Sides opposite to the equal angles are equal ]

⇒  AB=CD and AD=BC       [ Opposite sides of parallelogram are equal ]

∴   AB=BC=CD=AD  

Thus, all sides are equal. So, ABCD is a rhombus.

∴  The statement , diagonal of a parallelogram bisects one of its angle, then it is a rhombus it is correct.