Write whether the following statement is True or False? Justify your answer:

"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.

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Solution

Euclid's fifth Postulate: If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on-that side on which the sum of angles is less than two right angles.

Since it is an equivalent version of Euclid's fifth postulate, and it is known as Playfair's axiom.

Hence, the given statement is true.

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Similar questions

Q. 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.

Based on Playfair's axiom, for every line $' l'$ and every point $' P'$ not lying on $' l'$ , there exists ____ line(s) passing through $' P'$ and parallel to $' l'$ .

Is the statement “For every line $l$ and for every point P not lying on $l$ , there exists a unique line m passing through P and parallel to $l$ ”, true or false.

For every line $l$ and for every point P not lying on $l$ , there exists a unique line m passing through P and parallel to $l$ .

Q. For every line L and for every point P not lying on a given line L, there exists _____________ passing through P and parallel to L.

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Axioms

Standard VIII Mathematics

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Write whether the following statement is True or False? Justify your answer: "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.

Write whether the following statement is True or False? Justify your answer:

"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.