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Q.

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


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a

True

b

False 

answer is A.

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Detailed Solution

Given that AC=BD   ,
Question ImageWe need to prove that AB=CD   .
From the given figure, we note that the point B lies between A and C, so we get,
AC=AB+BC   ...... (1)
Also we note that the point C lies between B and D, so we get,
BD=BC+CD   ...... (2)
Now we have AC=BD   , we get,
AB+BC=BC+CD   ...... (3)
Using the Euclid's third axiom. It states that, ''when equals are subtracted from equals, the remainders are also equal.''
So we subtract BC from both sides of the equation (3), we get,
⇒AB+BC−BC=BC+CD−BC ⇒AB=CD  
Hence by using Euclid's third axiom, AB=CD   .
Therefore, option (1) is correct and the statement is true.
 
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