Question

Four sides of quadrilateral are equal, prove that its angles are bisected by the diagonals.

Answer 1



When all four sides of a quadrilateral are equal, then it is either a square or a rhombus.

Now, in both cases, the diagonals are perpendicular bisector of each other.

Again from the figure,

∠AOB = ∠BOC = ∠COD = ∠AOD = 90

and AB = BC = CD = DA

Now, from triangle AOB and BOC,

AO = OC

OB = OB   {common}

AB = CD    {given}

So, from SSS congruency,

ΔAOB ≅ ΔBOC

So, from CPCT,

∠OBA = ∠OBC

Hence, the diagonal BD bisects the ∠ABC.

Similarly, we can show that BD and AC also bisect other angles in the quadrilateral ABCD.

Hence, if all the sides of the quadrilateral are equal, then its angles are bisected by their diagonals.

Answer 2

Answer:

Step-by-step explanation: