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.
Euclid's Geometry
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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.

KnowledgeBoat · Accepted Answer

Let us consider that line segment AB has two midpoints C and D. Let's assume C to be the mid-point of AB. ∴ AC = BC Adding AC on both sides, we get : ⇒ AC + AC = BC + AC ⇒ 2AC = AB ⇒ AC = .............(1) Let's assume that D is another mid-point of AB. ∴ AD = BD Adding equal length AD on both sides, we get ⇒ AD + AD = BD + AD (BD + AD coincides to AB) ⇒ 2AD = AB ⇒ AD = .........(2) From equations (1) and (2), we get : ⇒ AC = AD. ⇒ C has to coincide with D for AC to be equal to AD. According to Euclid's Axiom 4: Things which coincide with one another are equal to one another. Hence, proved that a line segment has only one midpoint.

Mathematics

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.

Euclid's Geometry

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