“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l ” is known as Playfair’s axiom. Is the given statement true or false? Justify your answer
Solution:
Consider the lines l is parallel to the line m through a point P outside the line l
Consider n as another line that pass through P
From P a line PQ is drawn to Q on l
Let PQ make angle c with l and alternate angle a with m
As l and m is parallel
∠c = ∠a …. (1)
Consider another line n parallel to l and pass through P
Angle alternate to c made by n with PQ is b
As l and n are parallel
∠c = ∠b …. (2)
From Euclid’s first axiom
∠a = ∠b
Either ∠a is a part of ∠b or ∠b is a part of ∠a
From Euclid’s fifth axiom
∠a = ∠b
Therefore, the statement is true.
✦ Try This: Deepthi and Apeksha have the same weight. If they each gain weight by 13 kg, how will their new weights be compared ?
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 5
NCERT Exemplar Class 9 Maths Exercise 5.2 Problem 7
“For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l ” is known as Playfair’s axiom. Is the given statement true or false? Justify your answer
Summary:
The statement “For every line l and for every point P not lying on a given line l, there exists a unique line m passing through P and parallel to l ” is known as Playfair’s axiom is true
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