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Chapters
2: Parallel Lines
3: Triangles
4: Constructions of Triangles
5: Quadrilaterals
6: Circle
7: Co-ordinate Geometry
8: Trigonometry
9: Surface Area and Volume
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Solutions for Chapter 1: Basic Concepts in Geometry
Below listed, you can find solutions for Chapter 1 of Maharashtra State Board Balbharati for Mathematics 2 [English] Standard 9 Maharashtra State Board.
Balbharati solutions for Mathematics 2 [English] Standard 9 Maharashtra State Board 1 Basic Concepts in Geometry Practice set 1.1 [Page 5]
Find the distance with the help of the number line given below.
d(B, E)
Find the distance with the help of the number line given below.
d(J, A)
Find the distance with the help of the number line given below.
d(P, C)
Find the distance with the help of the number line given below.
d(J, H)
Find the distance with the help of the number line given below.
d(K, O)
Find the distance with the help of the number line given below.
d(O, E)
Find the distance with the help of the number line given below.
d(P, J)
Find the distance with the help of the number line given below.
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
From the information given below, find which of the point is between the other two. If the points are not collinear, state so.
d(L, M) = 11, d(M, N) = 12, d(N, L) = 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(X, Y) = 15, d(Y, Z) = 7, d(X, Z) = 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(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).
Sketch proper figure and write the answer of the following question.
If A- B - C and l(AC) = 11, l(BC) = 6.5, then l(AB) = ?
Sketch proper figure and write the answer of the following question.
If R-S-T and l(ST) = 3.7, l(RS) = 2.5, then l(RT) = ?
Sketch proper figure and write the answer of the following question.
If X-Y-Z and l(XZ) = `3sqrt7`, l(XY) = `sqrt7`, then l(YZ) = ?
Which figure is formed by three non-collinear points?
Balbharati solutions for Mathematics 2 [English] Standard 9 Maharashtra State Board 1 Basic Concepts in Geometry Practice set 1.2 [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 |
seg DE and seg AB
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 |
seg BC and seg AD
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 |
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.
- Write the name of the opposite ray of ray RP.
- Write the intersection set of ray PQ and ray RP.
- Write the union set of ray PQ and ray QR.
-
State the rays of which seg QR is a subset.
-
Write the pair of opposite rays with common end point R.
-
Write any two rays with common end point S.
-
Write the intersection set of ray SP and ray ST.
Answer the questions with the help of a given figure.
- State the points which are equidistant from point B.
- Write a pair of points equidistant from point Q.
- Find d(U, V), d(P, C), d(V, B), d(U, L).
Balbharati solutions for Mathematics 2 [English] Standard 9 Maharashtra State Board 1 Basic Concepts in Geometry Practice set 1.3 [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.
In an isosceles triangle, the segment joining the vertex and the mid point of the base is perpendicular to the base.
Write a converse of the following statement.
The alternate angles formed by two parallel lines and their transversal are congruent.
Write a converse 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 a converse of the following statement.
The diagonals of a rectangle are congruent.
Balbharati solutions for Mathematics 2 [English] Standard 9 Maharashtra State Board 1 Basic Concepts in Geometry Problem set 1 [Pages 11 - 12]
Select the correct alternative from the answers of the questions given below
How many mid points does a segment have?
only one
two
three
many
How many points are there in the intersection of two distinct lines?
infinite
two
one
not a single
How many lines are determined by three distinct points?
two
three
one or three
six
Find d(A, B), if co-ordinates of A and B are -2 and 5 respectively.
-2
5
7
3
If P - Q - R and d(P, Q) = 2, d(P, R) = 10, then find d(Q, R).
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, the co-ordinates of P, Q, R are 3, -5 and 6 respectively. State with reason whether the following statement is 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 statement is 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.
0, - 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 questions.
If A-B-C and d(A, C) = 17, d(B, C) = 6.5 then d(A, B) = ?
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.
Every rhombus is a square.
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.
If the sum of measures of angles in a figure is 180°, then the figure is a triangle.
Write the converse of the following statement.
If the sum of measures of two angles is 90° 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.
Two equilateral triangles are similar.
Draw a labelled figure showing information in the following statement and write the antecedent and the consequent.
If angles in a linear pair are congruent then each of them is a right angle.
Draw a labelled figure showing information in the following statement and write the antecedent and the consequent.
If the altitudes drawn on two sides of a triangle are congruent then those two sides are congruent.
Solutions for 1: Basic Concepts in Geometry
Balbharati solutions for Mathematics 2 [English] Standard 9 Maharashtra State Board chapter 1 - Basic Concepts in Geometry
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Concepts covered in Mathematics 2 [English] Standard 9 Maharashtra State Board chapter 1 Basic Concepts in Geometry are Concept of Lines, Planes, Concept of Points, Line Segments, Rays, Fundamentals of Geometrical Concepts, Co-ordinates of Points and Distance, Conditional Statements and Converse, Proofs, Betweenness.
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