Read the following statement: “A square is a polygon made up of four line segments, out of which, length of three line segments are equal to the length of fourth one and all its angles are right angles”. Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all angles and sides of a square are equal
Solution:
Given, the statement is “A square is a polygon made up of four line segments, out of which, length of three line segments are equal to the length of the fourth one and all its angles are right angles”.
We have to define the terms used in the definition.
We have to find the undefined terms
We have to justify that all angles and sides of a square are equal.
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.
Ray : any of a set of straight lines passing through one point.
Right Angle : an angle measures exactly 90 degrees (or π/2)
The undefined terms are point and line.
By Euclid’s postulate,
All right angles are equal to one another
Given, all the angles are right angles
From Euclid’s postulate, all angles are equal.
By Euclid’s axiom,
The things which are equal to the same thing are equal to one another.
Given, three line segments are equal to the fourth segment
Therefore, all the four sides of a square are equal.
✦ Try This: XZ and AB are parallel then, using proportionality theorem, find the value of YZ.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 5
NCERT Exemplar Class 9 Maths Exercise 5.4 Sample Problem 1
Read the following statement: “A square is a polygon made up of four line segments, out of which, length of three line segments are equal to the length of fourth one and all its angles are right angles”. Define the terms used in this definition which you feel necessary. Are there any undefined terms in this? Can you justify that all angles and sides of a square are equal
Summary:
For the following statement: “A square is a polygon made up of four line segments, out of which, the length of three line segments are equal to the length of the fourth one and all its angles are right angles”. 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 angles and sides of a square are equal
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