We know that △ OAB is an equilateral triangle
So it can be written as
∠ OAB = ∠ OBA = AOB = 60o
From the figure we know that ABCD is a square
So we get
∠ A = ∠ B = ∠ C = ∠ D = 90o
In order to find the value of ∠ DAO
We can write it as
∠ A = ∠ DAO + ∠ OAB
By substituting the values we get
90o = ∠ DAO + 60o
On further calculation
∠ DAO = 90o – 60o
By subtraction
∠ DAO = 30o
We also know that ∠ CBO = 30o
Considering the △ OAD and △ OBC
We know that the sides of a square are equal
AD = BC
We know that the sides of an equilateral triangle are equal
OA = OB
By SAS congruence criterion
△ OAD ≅ △ OBC
So we get OD = OC (c. p. c. t)
Therefore, it is proved that △ OCD is an isosceles triangle.