Page 6 - Lesson Notes-Euclid Definitions,Axioms and Postulates Ch-5(Introduction to Euclid')

terms of „metre‟ or Its parts.

Congruent Line Segment Length Axiom: Two congruent line segments have
equal length and conversely, two-line segments of equal length are congruent,

i.e., AB ≌ CD ⇔ l (AB) = l (CD).

Distance between Two Points: The distance between two points P and Q is the
length of the line segment joining them and it is denoted by PQ.

Betweenness: Point C is said to lie between the two points A and B, if

(a) A, B and C are collinear points and

(b) AC + CB = AB.

Mid-point of a Line Segment: Given a line segment AB, a point M is said to be the
mid-point of AB, if M is an interior point of AB such that AM = MB.

Line through M, other than line AB is called the bisector of the segment AB.

Example-1:

If a point C lies between two points A and B such that AC = BC, then prove that AC =

AB. Explain by drawing the figure.

Given, AC = BC.
Adding AC on both the sides, we get,
AC + AC = BC + AC – (i)
From the figure, we can see that, AB is the line segment part of two parts AC and
BC.
Thus, AB = AC + BC – (ii)
Substituting in (i), we get,
AC + AC = AB i.e. 2AC = AB

Hence, AC = AB

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