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State whether the statement is true or false.

If $AC = BD$ , then $AB = CD$ .

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False

True

answer is A.

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Detailed Solution

A straight set of points that extend in opposite directions is called Line.
A segment is the part of the line which has two endpoints.

AC = BD

…….(1)
As we know, Point B lies between A and C
Therefore,

……(2)
And point C lies between A and D
Therefore,

……(3)
Substituting the value of AC and BD from (2) and (3) in (1),

……(4)
We know, according to Euclid’s Axioms, If equals are subtracted from equals the remaining are equal.
Therefore, on subtracting BC in equation (4) on both sides, we get,

Thus, AB=CD.
Hence, option 1 is correct, and the given statement is true.

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