Q. 345.0( 3 Votes )

# Prove that every line segment has a unique mid-point.

Answer :

Let us consider, a line segment AB.

Assume that it has two midpoints say C and D

Midpoint of a line segment divides it into two equal parts

So, AC = BC and AD = DB

Since, C is midpoint of AB, we have A, C and B are collinear

Thus, AC + BC = AB ……………… (i)

Similarly, we get AD + DB = AB ……………(ii)

From eq(i) and (ii), we get

AC + BC = AD + DB

2 AC = 2AD

AC = AD

This is a contradiction unless C and D coincide.

Therefore our assumption that a line segment AB has two midpoints is incorrect.

Thus every line segment has one and only one midpoint.

Rate this question :

Show that every line segment has one and only one middle point.

RS Aggarwal & V Aggarwal - MathematicsFrom the given figure, name the following:

(A) Three lines

(B) One rectilinear figure

(C) Four concurrent points

RS Aggarwal & V Aggarwal - Mathematics

Which of the following is a statement or which of the following statement is true?

RS Aggarwal & V Aggarwal - MathematicsWhich is true?

RS Aggarwal & V Aggarwal - MathematicsWhich is false?

RS Aggarwal & V Aggarwal - MathematicsMatch the following columns.

The correct answers are:

RS Aggarwal & V Aggarwal - MathematicsProve that every line segment has a unique mid-point.

RS Aggarwal & V Aggarwal - MathematicsThe question consists of two statements, namely, Assertion (A) and Reason (R), Please select the correct answer.

The question consists of two statements, namely, Assertion (A) and Reason (R), Please select the correct answer.