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Q.

State whether the following is true or false.


Prove that an equilateral triangle can be constructed on any given line segment.


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a

True

b

False 

answer is A.

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Detailed Solution

An equilateral triangle is a triangle with all three sides of equal length.
Draw the line segment:
Construct the line segment with AC=AB   (Radii of the same circle) & BC=AB   (Radii of the same circle).
Question ImageUnderstand that, from Euclid's axiom, things which are equal to the same thing are equal.
Therefore,
⇒AC=BC ⇒AB=AC=BC  
Hence, triangle ABC is an equilateral triangle.
Therefore, option (1) is correct and the statement is true.
 
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