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

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True

False

answer is A.

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Detailed Solution

Given that

A C = B D

We need to prove that

A B = C D

.
From the given figure, we note that the point B lies between A and C, so we get,

A C = A B + B C

...... (1)
Also we note that the point C lies between B and D, so we get,

B D = B C + C D

...... (2)
Now we have

A C = B D

, we get,

A B + B C = B C + C D

...... (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,

⇒ A B + B C − B C = B C + C D − B C ⇒ A B = C D

Hence by using Euclid's third axiom,

A B = C D

.
Therefore, option (1) is correct and the statement is true.

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