Maths / Euclids Geometry / Euclid Axioms

QUESTION

If P, Q and R are three points on a line, and Q lies between P and R, then prove that PQ + QR = PR.

EXPLANATION
Explain TypeExplanation Content
Text

Given:  P , Q and R are three points on a line and Q lies between P and R

To Prove : PQ + QR = PR

Proof : Consider a point Q which lies between the points P and R of the line segment PR. Then it implies that PQ + QR will coincide with the line segment PR. Now, by using the Euclid's fourth axiom which states that things which coincide with each other are equal to each other.

So, By using Euclid's fourth axiom, We get PQ + QR = PR

Hence Proved

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