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Q.

State whether the following is true or false.

Look at the figure, then length AH > sum of lengths of AB + BC + CD.

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a

True

b

False

answer is A.

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Detailed Solution

Given is a figure,
Question Image

Euclid's axiom states that the whole is greater than the part.
Part of anything is always less than the whole.
Note the given conditions.
Now, we have different points B,C,D,E,F,G in line A to H.
We can write AD as- AB+BC+CD = AD ………..(1)
Now, we see in the figure AD is part of the line segment AH.
We use Euclid's algorithm which states that the whole is always greater than the part. Therefore, AH > AD.
Thus, length AH > sum of lengths AB + BC + CD.
Therefore, option (1) is correct and the statement is true.

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