Question

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

Answer 1

$\huge\underline\mathfrak{Answer:}$

Given a line segment AB of any length.

Using Euclid's postulate :- A circle may be drawn with any centre and any radius.

With A as center and AB of radius, draw a circle.

Similarly, with B as centre BA as the radius, draw another circle. Two circles meet at a point C.

Now, draw line segment AC and BC to form ∆ABC.

So, we have to prove that this triangle is equilateral, i.e., AB = AC = BC = .

Now, AB = AC, since they are the radii of the same circle.

Similarly, AB = BC (Radii of the same circle).

From these two facts and Euclid's Axiom that things which are equal to the same thing are equal to one another, we conclude that AB = BC = AC.

So, ABC is an equilateral triangle.

Answer 2

Step-by-step explanation:

Hope it helps you.