Euclid's Parallel Postulate and Playfair's Axiom

Q.

Choose the correct option:

Give two points in a plane, the number of lines which can be drawn to pass through these two points is _________

A. zero

B. exactly one

C. at most one

D. more than one

Q. 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. This statement is ________

1. Euclid's parallel axiom
2. Playfair's postulate
3. Euclid's postulate
4. Playfair's theorem

Q. Identify Playfair's postulate from the following :

1. 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.
2. 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.
3. 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.
4. 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°.

Q. The sum of angles of a triangle formed in a spherical geometry is equal to ${180}^o$

1. True
2. False

Q.

Choose the correct option:

Give a point on the plane, one can draw ____________

A. unique

B. two

C. finite number of

D. infinitely many lines through that point