Hint: Write AC as sum of 2 line segments generated by point B, similarly for BD.
It is been given in the question that $AC = BD$……………………………… (1) Now, it is clear from the figure that point B lies between A and C. So, we can say that $AC = AB + BC$…………………………….. (2) Now, again it is clear that point C lies between B and D. So, we can say that $BD = BC + CD$……………………………… (3) Now, let’s substitute equation (2) and equation (3) in equation (1) we get $ \Rightarrow AB + BC = BC + CD$ Simplifying it further, we get $ \Rightarrow AB + BC - BC = CD$ Therefore, $AB = CD$ Hence proved.
Note - In such questions always look for the point that is dividing the line segment and write the length of the entire segment in terms of that point.
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