Identify Playfair's postulate from the following :

If a transversal cuts two distinct straight lines in such a way that the sum of two interior angles on the same side of the transversal is equal to

180^{o}

, then the two lines are parallel to each other.

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If a straight line meets two other lines, so as to make the two interior angles on one side of it together less than two right angles, the other straight lines will meet if produced on that side on which the angles are less than two right angles.

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Given a line in a plane and a point outside the line in the same plane, there is a unique line passing through the given point and parallel to the given line.

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If a transversal cuts two parallel lines, then the sum of two interior angles on the same side of the transversal is equal to 180°.

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Solution

The correct option is C Given a line in a plane and a point outside the line in the same plane, there is a unique line passing through the given point and parallel to the given line.
Playfair was a Scottish mathematician who's postulate is a simple equivalent version of the parallel postulate of Euclid. Playfair's postulate states that- ' Given a line in a plane and a point outside the line in the same plane, there is a unique line passing through the given point and parallel to the given line.'

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Fill in the blanks in each of the following to make the statement true:
(i) If two parallel lines are intersected by a transversal then each pair of corresponding angles are ___
(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ___
(iii) Two lines perpendicular to the same line are ___ to each other.
(iv) Two lines parallel to the same line are to ___ each other.

(v) If a transversal intersects a pair of lines in such a way that a pair of alternate angles are equal, then the lines are ___
(vi) If a transversal intersects a pair of lines in such a way that the sum of interior angles on the same side of transversal is $180^{0}$ , then the lines are ___

Which of the following statements are true (I) and which are false (F)? Give reasons.
(i) If two lines are intersected by a transversal, then corresponding angles are equal.
(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
(iii) Two lines perpendicular to the same line are perpendicular to each other.
(iv) Two lines parallel to the same line are parallel to each other.
(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

Q. 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?

Q. Fill in the blank. 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 ___ two right angles.

Q. A transversal intersects two parallel lines. If one of interior angles is 60 degrees, other interior angle on the same side of transversal is equal to ____ degrees

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