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# In the figure, if AC=BD, then prove that AB=CD.

Last updated date: 18th Mar 2023
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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.