Postulate,Theorem and Proof

Q.

Only one line can pass through a single point. True or False?

1. True

2. False

Q.

Two lines are coincident if they have only one point in common. True or False?

1. True

2. False

Q.

A _______ has no end points.

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

Two distinct intersecting lines cannot be parallel to the same line.

1. True
2. False

Q. State whether the given statement is true or false.
An axiom is a statement that is obviously true whereas the statements which are particular to Geometry and accepted without question are known as postulates.

1. True
2. False

Q.

There are unlimited number of lines through a point.

1. True
2. False

Q. Find the consequent of the converse of: If a - b > 0, then a > b.
[2 Marks]

Q.

The number of lines that can pass through a given point is:

1. None

2. Infinitely many

3. Two

4. Only one

Q.

An infinite number of lines can pass through a given$\_\_\_\_\_$

Q. The co-ordinates of the point of reflection of the origin $(0,0)$ in the line $4x-2y-5=0$ is

1. $(-1,2)$
2. $(2,-1)$
3. $(\frac{4}{5},-\frac{2}{5})$
4. $(2,5)$

Q. A proof is required for a :

1. Postulate
2. Axiom
3. Theorem
4. Definition

Q. ________ lines can pass through a point.

1. 1
2. 2
3. 3
4. Infinite

Q.

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

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

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

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

4. 75${}^{\circ }$, 85${}^{\circ }$, 105${}^{\circ }$

Q. (1) Innovation is work.
(A) There are people who are clearly more talented innovators than the rest of us.
(B) It requires knowledge.
(C) It also requires great ingenuity.
(D) But that alone is not enough.
(6) And this is because they are able to imagine and conceive what we do not even consider possible.

1. BCAD
2. BDCA
3. CDBA
4. DBCA

Q. Akash draws a straight line on a sheet of paper. Then he draws another line such that the distance between the two is the same throughout. Similarly, he draws one more line in the same manner. He names these line as l, m and n. Which of the following is correct?

1. l $\perp$ m
2. m $\perp$ n
3. l $\parallel$ m $\parallel$ n
4. l $\parallel$ m only and m $\perp$ n

Q. Anmol was cutting a piece of paper with a pair of scissors. He observed that as he increases the angle of the scissors, then the vertically opposite angle ___.

1. Decreases by same amount

2. Remains constant

3. Increases by double

4. Increases by same amount

Q.

In the figure below, a ray OC extends from a point O on a straight line AB. If $\angle$AOC = ${135}^{\circ }$, then $\left(\frac{\angle BOC}{3}\right)$ is equal to :

1. ${15}^{\circ }$

2. ${65}^{\circ }$

3. ${20}^{\circ }$

4. ${45}^{\circ }$

Q. The sum of interior angles of a pair of parallel lines, formed by a line that intersects the parallel lines is

1. $0^{\circ }$
2. ${90}^{\circ }$
3. ${360}^{\circ }$
4. ${180}^{\circ }$

Q.

____________ line(s) can pass through a given points.

Q.

A_______ has no end points.

Q. _______ lines can pass through a point.

1. 2
2. 3
3. 4
4. Infinite

Q. _______ lines can pass through a point.

1. 2
2. 3
3. 4
4. Infinite

Q. Arrange in a logical order
G , S , D , A , F

1. ASDFG
2. ADGFS
3. AGDSF
4. DAGFS

Q. The universal truths that are very trivial and self-evident are called and postulates.

1. Axioms
2. Theorem
3. Identities

Q.

Vertically opposite angles are always:

1. Equal

2. Complementary

3. Supplementary

4. Not equal

Q. Identify Playfair's postulate from the following :

1. 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°.
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 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.