Choose the correct figure in the following:
Isosceles triangle can be constructed on any given line segment.
Using Postulate 2 (To produce a finite straight line continuously in a straight line), extend the line \(AB\) to a point \(D\) such that \(AD\) is greater than half of \(AB\).
In the statement above, a line segment of any length is given, say \(AB\) [see Fig.].
Using Euclid’s Postulate \(3\), you can draw a circle with point \(A\) as the centre and \(AB\) as the radius [see Fig.].
Similarly, draw another circle with point \(B\) as the centre and \(BA\) as the radius.
The two circles meet at a point, say \(C\).
Now, draw the line segments \(AC\) and \(BC\) to form \(∆ ABC\)
Now, we have to prove that this triangle is isosceles,
That is, \(AB = AC \).
since they are the radii of the same circle
From Euclid’s axiom that things which are equal to the same thing are equal to one another. We can conclude that \(AB = AC\). So, \(∆ ABC\) is an isosceles triangle.
That is, \(AB = AC \).
since they are the radii of the same circle
From Euclid’s axiom that things which are equal to the same thing are equal to one another. We can conclude that \(AB = AC\). So, \(∆ ABC\) is an isosceles triangle.