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 which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle
Solution:
Given, the statement is “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”.
We have to define the terms used in the definition.
We have to find the undefined terms
We have to justify that all the sides and all angles are equal in an equilateral triangle.
The terms used in the definition,
Polygon : a plane figure with at least three straight sides and angles, and typically five or more.
Line segment : a piece or part of a line having two endpoints
Angle : the space measured in degree, between two intersecting lines or surfaces at or close to the point where they meet.
Acute angle : an angle which measures less than 90 degrees
The undefined terms are point and line.
Given, two line segments are equal to the third one
All the angles are equal to 60° each
By using Euclid’s axiom,
The things which are equal to the same thing are equal to one another.
Therefore, all the three sides of an equilateral triangle are equal.
✦ Try This: Find the value of x.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 5
NCERT Exemplar Class 9 Maths Exercise 5.4 Problem 1
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 which you feel necessary. Are there any undefined terms in this? Can you justify that all sides and all angles are equal in a equilateral triangle
Summary:
For 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. The necessary terms used in this definition are defined.The undefined terms are point and line. By Euclid’s postulate and axiom, it is justified that all sides and all angles are equal in an equilateral triangle
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