In Figure, `X` and `Y` are two points on equal sides `A B` and `A C` of a `A B C` such that `A X=A Ydot` Prove that `X C=Y Bdot`

Explanation

To prove that \( XC = YB \) given that \( AX = AY \) and \( AB = AC \), we can follow these steps:

### Step 1: Identify the Given Information
We are given:
- \( AX = AY \) (the lengths from point A to points X and Y are equal)
- \( AB = AC \) (the lengths of sides AB and AC of triangle ABC are equal)
- Angle \( A \) is common to both triangles \( ABY \) and \( ACX \).

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