Question

The diagonals of a square are perpendicular bisects of each other.Prove the statement.

Answer 1

Proof: Consider ΔAOD and ΔAOB

 AD = AB (Sides of a square are equal).

 OD = OB (Diagonals of a square bisect each other).

 AO = AO (Common side)

∴Using SSS congruency rule, ΔAOD ≈ to ΔAOB

⇒∠AOD = ∠AOB.

As ∠AOD + ∠AOB = 1800

∴∠AOD = 900.

∴ AO ⊥ BD

Hence, AC ⊥ BD.

Answer 2

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