In the figure (ii) given below, O is the point in the interior of a square ABCD such that OAB is an equilateral triangle. Show that OCD is an isosceles triangle.

∠OAD = ∠DAB - ∠OAB = 90° - 60° = 30°.

Similarly,

∠OBC = ∠CBA - ∠OBA = 90° - 60° = 30°.

⇒ ∠OAD = ∠OBC.

AD = BC (As sides of squares are equal).

OA = OB (As OAB is equilateral triangle).

∴ △OAD ≅ △OBC by SAS axiom.

We know that corresponding parts of congruent triangles are equal.

∴ OD = OC.

Hence, proved that OD = OC i.e. OCD is an isosceles triangle.