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

Answer

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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.

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.

Last updated date: 25th Sep 2023

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