Question

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.

• A. True
• B. False
• C. Ambiguous
• D. Data Insufficient

Answer 1

The correct option is A True

Let the lines l is parallel to the line m through a point P outside the line l.

Let n be another line which passes through P.

A line PQ is drawn from P to a point Q on l.

Let PQ make angle c with l and the alternate angle a with m.

Since l & m are parallel

$\angle c=\angle a$..............(i).

Let another line n, which is parallel to l, pass through P and

the angle, alternate to c, made by n with PQ be b.

Since l & n are parallel

$\angle c=\angle b$..............(i).

Then, by Euclid's first axiom,

$\angle a=\angle b$

(from i & ii)

But either $\angle a$ is a part of $\angle b$ or

$\angle b$ is a part of $\angle a$

(Euclid's fifth Axiom)

$\therefore \angle a\ne \angle b.$

so Plafair's Axiom is true.

Ans- Option A.