wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Prove that a line segment have one and only one mid point

Open in App
Solution

Let us consider, a line segment AB.
Assume that it has two midpoints say C and D

Recall that the midpoint of a line segment divides it into two equal parts
That is AC = BC and AD = DB
Since C is midpoint of AB, we have A, C and B are collinear
∴ AC + BC = AB → (1)
Similarly, we get AD + DB = AB → (2)
From (1) and (2), 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.

flag
Suggest Corrections
thumbs-up
117
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Postulates
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon