First Four Postulates

Q.

If the HCF of 65 and 117 is expressible in the form 65m - 117, then the value of m is 4.

1. True
2. False

Q. What is the difference between an axiom and postulates

Q.

How to write sets in rule method or set builder form

Q.

What is lemma?

Q.

Euclid stated that 'all right angles are equal to each other', in the form of

(a) a definition

(b) an axiom

(c) a postulate

(d) a proof

Q.

State Euclids division lemma.

Q. Q.ln triangle ABC, right angled at C, if p is the length of the perpendicular from C to AB and a, b , c have their usual meanings, then prove that A. cp=ab B. 1/p2 = 1/a2 + 1/b2

Q. How many lines can be drawn through 2 distinct points?

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

Q. How many straight lines can pass through two distinct points?

1. Two straight lines
2. Three straight lines
3. One straight line
4. Infinite straight lines

Q.

A terminated line can be produced indefinitely on both the sides. True or False?

1. True

2. False

Q. For every line l and for every point P not lying on l, there exists a intersecting line(s) m passing through P and _____ to l.

1. perpendicular
2. intersecting
3. none of the above
4. parallel

Q. If equals are added to equals, the wholes are

1. Equal
2. greater
3. Equal or Greater
4. Lesser

Q.

Collinear and Coplanar points are the same thing.

1. True
2. False

Q.

Visualizing Euclid’s division algorithm, find the values of $a,b$ and $c.$

1. $a=11,b=8,c=4$

2. $a=12,b=12,c=3$

3. $a=13,b=11,c=2$

4. $a=10,b=12,c=5$

Q.

The number of line(s) passing through a point (3, 4) is (are):

1. Two

2. Only one

3. Three

4. Infinite

Q.

A circle can be drawn with any centre but with a fixed radius. This is the statement of:

1. Euclid's Postulate 3

2. Euclid's Postulate 4

3. Euclid's Postulate 2

4. Euclid's Postulate 1

Q.

Consider the two ‘postulates’ given below:

(i) Given any two distinct points A and B, there exists a third point C, which is between A and B.

(ii) There exists at least three points that are not on the same line.

Do these postulates contain any undefined terms? Are these postulates consistent?

Do they follow from Euclid’s postulates? Explain.

Q. In a quadrilateral ABCD AO and bo are the bisector of angle A and Angle B respectively prove that angle aob is equals to half of angle C plus half of angle d

Q.

All right angles are equal to one another.

1. True

2. False

Q.

Define the following terms:
(i) Line segment (ii) Collinear points
(iii) Parallel lines (iv) Intersecting lines
(v) Concurrent lines (vi) Ray

Q.

Use Euclid's division algorithm to find the HCF of: 196 and 38220

Q. Question 2(iii)
Some pictures (a) to (c) are given below. Tell which of them show:
$3\times \frac{3}{4}=2\frac{1}{4}$
a)

b)

c)

Q. State Euclid division Lemma.

Q.

What is Euclids Division Lemma?

Q. If 2x = 2y, then x = y. Mention the postulate used.

1. Things which coincide with one another are equal to one another.
2. Things which are equal to the same thing are equal to one another.
3. Things which are double of the same things are equal to one another.
4. The whole is greater than the part

Q. If line $l_1\perp l_2$ and $l_2\perp l_3$ then what is relationship between $l_1$ and $l_3$

1. $L_1$ is equal to $L_3$
   
2. $L_1$ is perpendicular to $L_3$
   
3. $L_1$ is parallel to $L_3$
   
4. $L_1$ intersects $L_3$
   

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. Postulates are the assumptions which are specific to geometry.

1. False
2. True

Q.

Which of the following statements are true and which are false? Give reasons for your answers.

(i) Only one line can pass through a single point.

(ii) There are an infinite number of lines which pass through two distinct points.

(iii) A terminated line can be produced indefinitely on both the sides.

(iv) If two circles are equal, then their radii are equal.

(v) In the following figure, if AB = PQ and PQ = XY, then AB = XY.

Q.

Which of the following is a true statement ?

(a) Only a unique line can be drawn to pass through a given point.

(b) Infinitely many lines can be drawn to pass through two given points.

(c) If two circles are equal, then their radii are equal.

(d) A line has a definite length.