Name: Euclid’s Fifth Postulate and the Equivalent
Uploaded: 2019-07-19
Duration: 8 min 53 s
Description: In this video, let's learn about Euclid’s Fifth Postulate and its significance. We will also learn about PLAYFAIR’S AXIOM, which is an equivalent form of the...

Question

Using the postulate of drawing a circle, show that an equilateral triangle can be drawn with a given line segment as a side.

Accepted Answer

Take a line segment of any length is given, say $A B$ .

Euclid’s Postulate $3$ states that a circle can be drawn with any centre and a radius.

Using Euclid’s Postulate $3$ , we can draw a circle with point $A$ as the centre and $A B$ as the radius.

Similarly, draw another circle with point $B$ as the centre and $B A$ as the radius.

The two circles meet at a point, say $C$ . Now, draw the line segments $B C$ and $A C$ to form $△ A B C$ .

Now, $A B = A C$ , since they are the radii of the same circle.

Similarly, $A B = B C$ (Radii of the same circle)

Euclid’s axiom states that things which are equal to the same thing are equal to one another.

Therefore, $A B = B C = A C$

Hence, $△ A B C$ is an equilateral triangle.

Using the postulate of drawing a circle, show that an equilateral triangle can be drawn with a given line segment as a side.

Important Questions on Introduction to Euclid's Geometry

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