`O A\ =\ O B``a n d\ O D\ =\ O C`. Show that `(i) DeltaA O D~=DeltaB O C ` and `(ii) A D\ ||\ B C `

Explanation

To solve the problem, we need to show that triangles \( \Delta AOD \) and \( \Delta BOC \) are congruent and that lines \( AD \) and \( BC \) are parallel. Let's break this down step by step.

### Step 1: Given Information
We are given that:
- \( \angle O A = \angle O B \) (let's denote this as \( x \))
- \( \angle O D = \angle O C \) (let's denote this as \( y \))

### Step 2: Identify Angles in Triangles
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