Fifth Postulate and Playfair's Axiom

Q.

Prove that a line segment have one and only one mid point

Q.

How would you rewrite Euclid's fifth postulate so that it would be easier to understand ?

Q. If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

Q.

Point C is called a mid-point of line segment AB. Prove that every line segment has one and only one mid-point.

Q. Two line segments are said to be congruent if they have __.

Q. In how many points, can two distinct lines at most intersect?

1. Two points
2. One point
3. Infinite no. of points
4. Two lines cannot intersect each other.

Q.

Which one of the following statement is true?

1. Only one line can pass through a single point

2. If two circles are equal, then their radii are not equal

3. There are an infinite number of lines which pass through two distinct points

4. Two distinct lines cannot have more than one point in common

Q.

Does Euclid’s fifth postulate imply the existence of parallel lines? Explain.

Q.

Euclids fifth postulate states that if a straight line falling on two straight lines makes (P) angles on the same side of it taken together (Q) than two right angles, then the two straight lines, if produced indefinitely, meet on (R) side on which the sum of angles is (S) than two right angles.

1. (P) - interior, (Q) - less, (R) - opposite, (S) - greater.

2. (P) - interior, (Q)-less, (R) - same, (S) - less.

3. (P)-exterior, (Q)-greater, (R)-opposite, (S) - less.

4. (P) - exterior, (Q) - less, (R) - same, (S)- greater.

Q. If l, m, n are three lines such that l || m and n $\perp$ l. prove that n $\perp$ m.

Q. In each of the two lines is perpendicular to the same line, what kind of lines are they to each other?

Q.

Locate $\sqrt{10}$ on number line.

Q. Question 2
In the given figure, lines XY and MN intersect at O. If $\angle POY={90}^{\circ }$ and a:b = 2:3, find c.

Q.

Two distinct points always determine a line. True or False?

1. True

2. False

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. 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. Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.

Q. In the given figure, if lines AB and CD meet each other when extended towards A or C, then the relation between $\angle 1\text{and}\angle 2$ is .

1. (∠1 +∠2) = 180°
2. (∠1 +∠2) < 180°
3. (∠1 +∠2) > 180°

Q.

Given a line and a point, not on the line, there is one and only_____line which passes through the given point and is _____to the given line.

Q.

Two parallel lines l and m are such that A, C are the points on l and B, D are the points on m. AB and CD are perpendicular to both l and m. If AB = 4 cm, then CD =

1. 2 cm

2. 8 cm

3. 1 cm

4. 4 cm

Q.

A ............... is a surface which lies evenly with the straight lines on itself.

1. plane surface

2. three-dimensional surface

3. curved surface

4. none of these

Q. how to derieve that there are 4pi steradians in a sphere (solid angle)

Q.

Statement $1$: When two lines intersect each other, only the angles forming the linear pair are supplementary.

Statement $2$: When two lines intersect each other, angles forming the linear pair are supplementary.

Choose one or more correct option(s).

1. Both the statements are right.

2. Statement 1 is right but statement 2 is wrong.

3. Statement 2 is right but statement 1 is wrong.

4. Both the statements are wrong.

Q. In the given figure, rays OA and OB stand on a line POQ. The value of $x$ is:

1. ${20}^o$
2. ${25}^o$
3. ${30}^o$
4. ${35}^o$

Q.

Fill in the blanks :

A straight angle equals ____ right angles.

Q. Which of the following is not true about a straight line segment?

1. A straight line segment can be drawn joining any two points.
2. Any straight line segment can be extended indefinitely in a straight line.
3. Given any straight line segment, a circle can be drawn having the segment as diameter and any point as the centre.
4. A straight line segment is a one dimensional entity.

Q.

What is the Measure of a right angle and a straight angle?

Q. Does Euclid' fifth postulate imply the existence of parallel lines? Explain

1. True
2. False

Q.

In the figure below, lines XY and MN intersect at point O. If $\angle$POY = ${90}^{\circ }$ and A:B = 2:3, find $\frac{C}{2}$.

1. ${55}^{\circ }$

2. ${68}^{\circ }$

3. ${77.5}^{\circ }$

4. ${63}^{\circ }$

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.