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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True

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

A C = A B

(Radii of the same circle) &

B C = A B

(Radii of the same circle).
Question Image

Understand that, from Euclid's axiom, things which are equal to the same thing are equal.
Therefore,

⇒ A C = B C ⇒ A B = A C = B C

Hence, triangle ABC is an equilateral triangle.
Therefore, option (1) is correct and the statement is true.

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