5. in Question 4, Point C is Called a Mid-point of Line Segment Exercise 5.1 Chapter 5 Introduction to Euclid’s

5. In Question 4, point C is called a mid-point of line segment AB. Prove that every lin Chapter 5: Introduction to Euclid’s Geometry Maths Class 9 solutions are developed for assisting understudies with working on their score and increase knowledge of the subjects. 5. In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point. is solved by our expert teachers. You can get ncert solutions and notes for class 9 chapter 5 absolutely free. NCERT Solutions for class 9 Maths Chapter 5: Introduction to Euclid’s Geometry is very essencial for getting good marks in CBSE Board examinations

5. In Question 4, point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.
Let C and D are two midpoints of the line segments AB
According to Euclid’s axioms 4
AC      = BC               ...(1)
D is also a mid point so that
AD      = DB               … (2)
We have                    AB       = AB               … (3)
And we know           AB       = AC + CB
AB       = AD + DB
From equation (iii)
AC + CB        = AD + DB
From equation (1) and (2)plug the value of BC and DB we get
AC +AC         = AD +AD
2AC    = 2AD
Divide by 2 we get
AC      = AD
Both points are on same line so both points will superimpose and D and C are exactly at the same place
Hence midpoint of the lines segment is always unique