Fifth Postulate and Playfair's Axiom

Q.

For the given statements select the correct option.

Assertion : Two lines are parallel if the sum of the co-interior angles made with the transversal is equal to 180°.

Reason : Two distinct lines cannot have more than one point in common

1. Assertion is true but reason is false.

2. Assertion is false but reason is true.

3. Both assertion and reason are true and reason is the correct explanation of assertion.

4. Both assertion and reason are true but reason is not the correct explanation of assertion.

Q.

The lines $\stackrel{⟷}{XW}$ and $\stackrel{⟷}{YZ}$ are parallel.

1. True

2. False

Q. Anmol was cutting a piece of paper with a pair of scissors. She observed that as she increased the angle of the scissors, the angles created in the opposite arms(vertically opposite angle) ___.

1. Increases by same amount

2. Decreases by same amount

3. Remains constant

4. Increases by double

Q.

Find the measure of $\angle$2, $\angle$3 and $\angle$4 from the given figure.

1. 75${}^{\circ }$, 75${}^{\circ }$, 105${}^{\circ }$

2. 75${}^{\circ }$, 85${}^{\circ }$, 105${}^{\circ }$

3. 105${}^{\circ }$, 75${}^{\circ }$, 75${}^{\circ }$

4. 105${}^{\circ }$, 75${}^{\circ }$, 105${}^{\circ }$

Q.

In the below-given figure, there are ___ transversals.

Q.

In the figure given below identify interior angles.

1. $\angle$3, $\angle$4, $\angle$5, $\angle$6.

2. $\angle$1, $\angle$2, $\angle$8, $\angle$7.

3. $\angle$3, $\angle$2, $\angle$5, $\angle$6.

4. $\angle$1, $\angle$2, $\angle$3, $\angle$4.

Q.

In the figure below, OP, OQ, OR and OS are four rays. Then, find $\frac{(\angle POQ+\angle QOR+\angle SOR+\angle POS)}{3}$.

1. 

2. 

3. 

4. 

Q. Identify Playfair's postulate from the following :

1. 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.
2. 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.
3. 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.
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.

Which of the following option(s) is/are correct when a transversal intersects two parallel lines?

1. Corresponding angles are equal
2. Alternate angles are equal
3. Vertically opposite angles are equal
4. Complementary angles are equal

Q. A line that intersects two lines at distinct points is called as ___.