# R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 6 - Introduction to Euclid's Geometry

## Chapter 6 - Introduction to Euclid's Geometry Exercise MCQ

Correct option: (b)

Squares and circular altars were used for household rituals.

Whereas altars having shapes as combinations of rectangles, triangles and trapeziums were used for public worship.

Correct option: (b)

In ancient India, altars with combination of shapes like rectangles, triangles and trapeziums were used for public rituals.

Correct option: (c)

The Sriyantra consists of nine interwoven isosceles triangles.

Correct option: (b)

In Indus Valley Civilization (about 300 BC) the bricks used for construction work were having dimensions in the ratio is 4:2:1.

Correct option: (a)

The famous treatise 'The Elements' was divided into 13 chapters by Euclid.

Correct option: (b)

Euclid belongs to the country, Greece.

Correct option: (c)

Thales belongs to the country, Greece.

Correct option: (b)

Pythagoras was a student of Thales.

Correct option: (d)

A statement that requires a proof is called a theorem.

Correct option: (a)

'Lines are parallel if they do not intersect' is started in the form of a definition.

Correct option: (c)

Euclid stated that 'All right angles are equal to each other' in the form of a postulate.

This is Euclid's Postulate 4.

Note: The answer in the book is option (a). But if you have a look at the Euclid's postulate, the answer is **a postulate**.

Correct option: (d)

A pyramid is a solid figure, whose base is any polygon.

Correct option: (a)

The side faces of a pyramid are triangles.

Correct option: (c)

A solid has 3 dimensions.

Correct option: (b)

A surface has 2 dimensions.

Correct option: (a)

A point is an exact location. A fine dot represents a point. So, a point has 0 dimensions.

Correct option: (c)

Boundaries of solids are surfaces.

Correct option: (b)

Boundaries of surfaces are curves.

Correct option: (d)

The number of planes passing through three non-collinear points is 1.

Correct option: (d)

Axioms are assumed as universal truths in all branches of mathematics because they are taken for granted, without proof.

Correct option: (c)

Two lines are said to be parallel, if they have no point in common.

Options (a), (b) and (d) have a common point, hence they are not parallel.

In option (c), the floor and the ceiling of a room are parallel to each other is a true statement.

Correct option: (c)

In option (a), infinite number of line can be drawn to pass through a given point. So, it is not a true statement.

In option (b), only one line can be drawn to pass through two given points. So, it is not a true statement.

In option (c),

'If two circles are equal, then their radii are equal' is the true statement.

In option (d), A line has no end points. A line has an indefinite length. So, it is not a true statement.

Correct option: (c)

Option (a) is true, since we can pass an infinite number of lines through a given point.

Option (b) is true, since a unique line can be drawn to pass through two given points.

Consider option (c).

As shown in the above diagram, a ray has only one end-point. So, option (d) is true.

Hence, the only false statement is option (c).

Correct option: (c)

A point C is called the midpoint of a line segment , if C is an interior point of AB such that =.

Correct option: (d)

Observe the above figure. Clearly, C lies between A and B if AC + CB = AB.

That means, points A, B, C are collinear.

Correct option: (b)

Euclid's second axiom states that 'If equals are added to equals, the wholes are equal'.

Hence, when x + y = 15, then x + y + z = 15 + z.

Correct option: (a)

Euclid's first axiom states that 'Things which are equal to the same thing are equal to one another'.

That is,

A's age = B's age and C's age = B' age

⇒ A's age = C's age

## Chapter 6 - Introduction to Euclid's Geometry Exercise Ex. 6

A theorem is a statement that requires a proof. Whereas, a basic fact which is taken for granted, without proof, is called an axiom.

Example of Theorem: Pythagoras Theorem

Example of axiom: A unique line can be drawn through any two points.

(i) Line segment: The straight path between two points is called a line segment.

(ii) Ray: A line segment when extended indefinitely in one direction is called a ray.

(iii) Intersecting Lines: Two lines meeting at a common point are called intersecting lines, i.e., they have a common point.

(iv) Parallel Lines: Two lines in a plane are said to be parallel, if they have no common point, i.e., they do not meet at all.

(v) Half-line: A ray without its initial point is called a half-line.

(vi) Concurrent lines: Three or more lines are said to be concurrent, if they intersect at the same point.

(vii) Collinear points: Three or more than three points are said to be collinear, if they lie on the same line.

(viii) Plane: A plane is a surface such that every point of the line joining any two points on it, lies on it.

(i) Six points: A,B,C,D,E,F

(ii)
Five line segments: _{}

(iii)
Four rays: _{}

(iv)
Four lines: _{}

(vi) Four collinear points: M,E,G,B

(i) _{} and their corresponding point of intersection is R.

_{} and their corresponding point of intersection is P.

(ii)
_{} and their point of intersection is R.

(iii) Three rays are:

_{}.

(iv) Two line segments are:

_{}.

(i) Three lines: Line AB, Line PQ and Line RS

(ii) One rectilinear figure: EFGC

(iii) Four concurrent points: Points A, E, F and B

(i) An infinite number of lines can be drawn to pass through a given point.

(ii) One and only one line can pass through two given points.

(iii) Two given lines can at the most intersect at one and only one point.

(iv)
_{}

(i) False

(ii) False

(iii) False

(iv) True

(v) False

(vi) True

(vii) True

(viii) True

(ix) True

(x) True

(xi) False

(xii) True

(ii) BL = BM

⇒ 2BL = 2BM

⇒ AB = BC

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