Easy
If $P$,$Q$,and $R$ are three points on a line,and $Q$ lies between $P$ and $R$ [see figure],then prove that $PQ + QR = PR$.
(N/A) In the figure given above,the line segment $PR$ coincides with the sum of line segments $PQ$ and $QR$.
Euclid's axiom $(4)$ states that things which coincide with one another are equal to one another.
Therefore,it can be deduced that $PQ + QR = PR$.
Note that,in this solution,it has been assumed that there is a unique line passing through two distinct points.
Euclid's axiom $(4)$ states that things which coincide with one another are equal to one another.
Therefore,it can be deduced that $PQ + QR = PR$.
Note that,in this solution,it has been assumed that there is a unique line passing through two distinct points.
Explore More
Similar Questions
State whether the following statement is True or False. Justify your answer.
If the area of a triangle equals the area of a rectangle and the area of the rectangle equals that of a square,then the area of the triangle also equals the area of the square.
If the area of a triangle equals the area of a rectangle and the area of the rectangle equals that of a square,then the area of the triangle also equals the area of the square.
Easy
View Solution$A$ statement that needs a proof is called a........
Easy
View SolutionSolve the following question using an appropriate Euclid's axiom:
In the figure,we have $\angle 1 = \angle 2$ and $\angle 2 = \angle 3$. Show that $\angle 1 = \angle 3$.
In the figure,we have $\angle 1 = \angle 2$ and $\angle 2 = \angle 3$. Show that $\angle 1 = \angle 3$.
Easy
View SolutionRead the following statements which are taken as axioms:
$(i)$ If a transversal intersects two parallel lines,then corresponding angles are not necessarily equal.
$(ii)$ If a transversal intersects two parallel lines,then alternate interior angles are equal.
Is this system of axioms consistent? Justify your answer.
$(i)$ If a transversal intersects two parallel lines,then corresponding angles are not necessarily equal.
$(ii)$ If a transversal intersects two parallel lines,then alternate interior angles are equal.
Is this system of axioms consistent? Justify your answer.
Easy
View Solution'Lines are parallel if they do not intersect' is stated in the form of
Easy
View SolutionVedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo