#### Chapters

#### Balbharati Balbharati Class 9 Mathematics 2 Geometry

## Chapter 1: Basic Concepts in Geometry

#### Chapter 1: Basic Concepts in Geometry Exercise Practice set 1.1 solutions [Page 5]

Find the distances with the help of the number line given below.

(i) d(B,E)

(ii) d(J, A)

(iii) d(P, C)

(iv) d(J, H)

(v) d(K, O)

(vi) d(O, E)

(vii) d(P, J)

(viii) d(Q, B)

If the co-ordinate of A is x and that of B is y, find d(A, B).

x = 1, y = 7

If the co-ordinate of A is x and that of B is y, find d(A, B).

x = 6, y = - 2

If the co-ordinate of A is x and that of B is y, find d(A, B).

x = - 3, y = 7

If the co-ordinate of A is x and that of B is y, find d(A, B).

x = - 4, y = - 5

If the co-ordinate of A is x and that of B is y, find d(A, B).

x = - 3, y = - 6

If the co-ordinate of A is x and that of B is y, find d(A, B).

x = 4, y = - 8

From the information given below, find which of the point is between the other two. If the points are not collinear, state so.

d(P, R) = 7, d(P, Q) = 10, d(Q, R) = 3

From the information given below, find which of the point is between the other two.

If the points are not collinear, state so.

d(R, S) = 8, d(S, T) = 6, d(R, T) = 4

From the information given below, find which of the point is between the other two.

If the points are not collinear, state so.

d(A, B) = 16, d(C, A) = 9, d(B, C) = 7

If the points are not collinear, state so.

d(L, M) = 11, d(M, N) = 12, d(N, L) = 8

If the points are not collinear, state so.

d(X, Y) = 15, d(Y, Z) = 7, d(X, Z) = 8

If the points are not collinear, state so.

d(D, E) = 5, d(E, F) = 8, d(D, F) = 6

On a number line, points A, B and C are such that d(A,C) = 10, d(C,B) = 8 . Find d(A, B) considering all possibilities.

Points X, Y, Z are collinear such that d(X,Y) = 17, d(Y,Z) = 8, find d(X,Z) .

Which figure is formed by three non-collinear points?

#### Chapter 1: Basic Concepts in Geometry Exercise Practice set 1.2 solutions [Pages 7 - 8]

The following table shows points on a number line and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not.

Point | A | B | C | D | E |

Co-ordinate | 3 | 5 | 2 | 7 | 9 |

(i) seg DE and seg AB

(ii) seg BC and seg AD

(iii) seg BE and seg AD

Point M is the midpoint of seg AB. If AB = 8 then find the length of AM.

Point P is the midpoint of seg CD. If CP = 2.5, find l(CD).

If AB = 5 cm, BP = 2 cm and AP = 3.4 cm, compare the segments.

Write the answers to the following questions with reference in the given figure.

(iii) Write the union set of ray PQ and ray QR.

Answer the questions with the help of a given figure.

#### Chapter 1: Basic Concepts in Geometry Exercise Practice set 1.3 solutions [Page 11]

**Write the following statement in ‘if-then’ form.**

The opposite angles of a parallelogram are congruent.

**Write the following statement in ‘if-then’ form.**

The diagonals of a rectangle are congruent.

**Write the following statement in ‘if-then’ form.**

**Write converses of the following statement.**

The alternate angles formed by two parallel lines and their transversal are congruent.

**Write converses of the following statement.**

If a pair of the interior angles made by a transversal of two lines are supplementary then the lines are parallel.

**Write converses of the following statement.**

The diagonals of a rectangle are congruent.

#### Chapter 1: Basic Concepts in Geometry solutions [Pages 11 - 12]

**Select the correct alternative from the answer of the question given below.**

How many mid points does a segment have?

only one

two

three

many

**Select the correct alternative from the answer of the question given below.**

infinite

two

one

not a single

**Select the correct alternative from the answer of the question given below.**

two

three

one or three

six

**Select the correct alternative from the answer of the question given below.**

-2

5

7

3

**Select the correct alternative from the answer of the question given below.**

12

8

`sqrt(96)`

20

On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.

d(P,Q) + d(Q,R) = d(P,R)

True

False

On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is true or false.

d(P,R) + d(R,Q) = d(P,Q)

True

False

On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statements are true or false.

d(R,P) + d(P,Q) = d(R,Q)

True

False

On a number line, co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statements are true or false.

d(P,Q) - d(P,R) = d(Q,R)

True

False

Co-ordinates of the pair of a point is given below. Hence find the distance between the pair.

3, 6

Co-ordinates of the pair of points are given below. Hence find the distance between the pair.

-9, -1

Co-ordinates of the pair of points are given below. Hence find the distance between the pair.

-4, 5

Co-ordinates of the pair of points are given below. Hence find the distance between the pair.

x, -2

Co-ordinates of the pair of points are given below. Hence find the distance between the pair.

x + 3, x - 3

Co-ordinates of the pair of points are given below. Hence find the distance between the pair.

-25, -47

Co-ordinates of the pair of points are given below. Hence find the distance between the pair.

80, - 85

Co-ordinate of point P on a number line is - 7. Find the co-ordinates of points on the number line which are at a distance of 8 units from point P.

Answer the following question.

If A - B - C and d(A,C) = 17, d(B,C) = 6.5 then d(A,B) = ?

Answer the following question.

If P - Q - R and d(P,Q) = 3.4, d(Q,R)= 5.7 then d(P,R) = ?

Co-ordinate of point A on a number line is 1. What are the co-ordinates of points on the number line which are at a distance of 7 units from A?

**Write the following statement in conditional form.**

**Write the following statement in conditional form.**

Angles in a linear pair are supplementary.

**Write the following statement in conditional form.**

A triangle is a figure formed by three segments.

**Write the following statement in conditional form.**

A number having only two divisors is called a prime number.

**Write the converse of the following statement.**

^{0}, then the figure is a triangle.

**Write the converse of the following statement.**

If the sum of measures of two angles is 90^{0} then they are complement of each other.

**Write the converse of the following statement.**

If the corresponding angles formed by a transversal of two lines are congruent then the two lines are parallel.

**Write the converse of the following statement.**

If the sum of the digits of a number is divisible by 3 then the number is divisible by 3.

**Write the antecedent (given part) and the consequent (part to be proved) in the following statement.**

If all sides of a triangle are congruent then its all angles are congruent.

**Write the antecedent (given part) and the consequent (part to be proved) in the following statement.**

The diagonals of a parallelogram bisect each other.

**Draw a labelled figure showing information in the following statement and write the antecedent and the consequent.**

**Draw a labelled figure showing information in the following statement and write the antecedent and the consequent.**

**Draw a labelled figure showing information in the following statement and write the antecedent and the consequent.**

## Chapter 1: Basic Concepts in Geometry

#### Balbharati Balbharati Class 9 Mathematics 2 Geometry

#### Textbook solutions for Class 9

## Balbharati solutions for Class 9 Geometry chapter 1 - Basic Concepts in Geometry

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Concepts covered in Class 9 Geometry chapter 1 Basic Concepts in Geometry are Proofs, Conditional Statements and Converse, Basic concept of segment, ray and line, Co-ordinates of points and distance, Basic Concept in Geometry.

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