Question

Read the following statement: An equilateral triangle is a polygon made up of three line segments out of which two line segments are equal to the third one and all its angles are 60° each. Define the terms used in this definition that you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in an equilateral triangle?

Answer 1

Step 1 : Defined terms are listed below:

$\left(1\right)$ Equilateral triangle: An equilateral triangle is a triangle with all three sides of equal length and all angles equal.

$\left(2\right)$ Polygon: A plane closed geometric figure with a minimum of three straight sides and angles.

$\left(3\right)$ Line segment: A line segment is a part of a line consisting of two endpoints.

$\left(4\right)$ Angle: The shape formed by two rays meeting at a common endpoint is called an angle.

$\left(5\right)$ Acute angles: The angle whose measures are less than $90°$ are called acute angles.

Step 2 : Undefined terms are:

$\left(1\right)$ Line

$\left(2\right)$ Point

According to Euclid’s axiom, things that are equal to the same thing are equal to one another.

Here, the angles of the equilateral triangle are $60°$ and two line segments are equal to the third one.

Therefore, by using Euclid’s axiom, all three sides and angles of an equilateral triangle are equal.