`P` is a point on the bisector of `angle ABC ` .If the line through `P`, parallel to `BA` meet at `Q` ,prove that ` Delta BPQ ` is an isosceles triangle.

Explanation

To prove that triangle \( \Delta BPQ \) is an isosceles triangle, we will follow these steps:

### Step 1: Identify the Given Information
We are given that \( P \) is a point on the bisector of angle \( ABC \) (which is \( BP \)). A line through \( P \) is drawn parallel to \( BA \) and meets \( BC \) at point \( Q \).

### Step 2: Use the Property of Parallel Lines
Since \( PQ \) is parallel to \( AB \), we can use the properties of alternate interior angles. The line \( BP \) acts as a transversal to the parallel lines \( PQ \) and \( AB \).

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