Visualising Solid Shapes Class 7 Notes Maths Chapter 15

Visualising Solid Shapes Class 7 NotesOn this page, you will find Visualising Solid Shapes Class 7 Notes Maths Chapter 15 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 15 Visualising Solid Shapes will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 15 Notes Visualising Solid Shapes

Visualising Solid Shapes Class 7 Notes Conceptual Facts

Solid Shapes:
1. Cuboid: Cuboid has length, breadth and height.
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .1

2. Cube: Cube has all sides equal.
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .2

3. Prism:
(i) Triangular prism:
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .3

(ii) Rectangular prism:
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .4

4. Pyramid:
(i) Triangular pyramid
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .5

(ii) Rectangular pyramid:
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .6

5. Tetrahedron: A triangle pyramid whose all the face are equilateral triangles of same size.

6. Cylinder:
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .7

7. Cone
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .8

8. Sphere:
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .9

Euler’s Formula:
V + F – E = 2
Net of 3-D shapes: Net is an arrangement of figures connected with their edges in the same plane.

(i) Net of cube:
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .10

(ii) Net of  Cylinder
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .12

(iii) Net of pyramid:
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .11

(iv) Net of Cone
Visualising Solid Shapes Class 7 Notes Maths Chapter 15 .13

Rational Numbers Class 7 Notes Maths Chapter 9

Rational Numbers Class 7 NotesOn this page, you will find Rational Numbers Class 7 Notes Maths Chapter 9 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 9 Rational Numbers will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 9 Notes Rational Numbers

Rational Numbers Class 7 Notes Conceptual Facts

1. Rational numbers: The number which are in the form of \(\frac{p}{q}\) where p and q are co-prime and
q ≠ 0 are called rational numbers.

2. All integers and fractions are rational numbers.

3. When we compare two integers, we need rational numbers.
e.g. 2 : 3 = \(\frac{2}{3}\) a rational number.

4. 0 is a rational number.

5. A rational number is said to positive if both of the numerator and denominator are either positive or negative.
\(\text { e.g. } \frac{5}{6}, \frac{-2}{-3}, \frac{0}{2} \text { etc }\)

6. A rational number is said to be negative if one of the numerator or denominator is negative.
\(\text { e.g. } \frac{-1}{2}, \frac{3}{-5}, \frac{0}{-1} \text { etc. }\)

7. Every integer is a rational number but every rational number need not to be an integer.

Properties of rational numbers:
(i) Equivalence of rational numbers: If \(\frac{p}{q}\) is a rational number and m is a not zero integer, then
Rational Numbers Class 7 Notes Maths Chapter 9

(ii) Reducting a rational number to its simplest form: a rational number and m is a common p+m r divisor top and q then \(\frac{p}{q}\), where H.C.F. of r and s is 1.
Rational Numbers Class 7 Notes Maths Chapter 9.1

Standard form of a rational number: A rational number is said to be in standard form if its denominator
Rational Numbers Class 7 Notes Maths Chapter 9.2

Rational numbers between two rational numbers:
There are unlimited rational numbers between two rational numbers.

Rational numbers on a number line.

  • Mark a point O on a straight line already marked with arrows at its end points.
  • Mark points on the line at unit length interval from each other on both sides like 1, 2, 3, … on right side of 0 and -3,-2, 1 on its left side.
  • To represent rational number \(\frac{2}{3} \text { and }-\frac{1}{2}\) on a number line.
    Rational Numbers Class 7 Notes Maths Chapter 9.4

Since \(\frac{2}{3}\) < 1
∴ Divide the first unit into three equal parts and mark division 2 by A which represent a rational 2
number \(\frac{2}{3}\). Similarly, divide the first unit on the left into two equal parts. Mark the middle one
3 1 by B which represents a rational number –\(\frac{2}{3}\).

Absolute value of a rational number: The absolute value of a rational number |a| is written as which shows its numerical value only regardless of its sign.
eg,…
Rational Numbers Class 7 Notes Maths Chapter 9.5

Symmetry Class 7 Notes Maths Chapter 14

Symmetry Class 7 NotesOn this page, you will find Symmetry Class 7 Notes Maths Chapter 14 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 14 Symmetry will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 14 Notes Symmetry

Symmetry Class 7 Notes Conceptual Facts

Symmetry; If a paper is folded in half and the two halves of the paper exactly cover each other, then the shape of the paper is symmetric.
For example:
Symmetry Class 7 Notes Maths Chapter 14 .1
Axis of symmetry: When a figure is folded in half then the line of fold is called axis of symmetry.
For example:
Symmetry Class 7 Notes Maths Chapter 14 .2

Symmetry of regular polygons:
Symmetry Class 7 Notes Maths Chapter 14 .3

Note: Each regular polygon has a many lines of symmetry as it has sides.

Mirror reflection symmetry: The symmetry in which one half of the shape is the image of the other.
For example:
Symmetry Class 7 Notes Maths Chapter 14 .4

Rotational symmetry: When an object rotate clockwise or anticlockwise about a fixed point and when it looks after some rotation by a partial turn then it is called rotational symmetry. This fixed point is known as centre of rotation.
Symmetry Class 7 Notes Maths Chapter 14 .5

Axis of rotation: The line of symmetry about of which an object rotates is called the axis of rotation.
Symmetry Class 7 Notes Maths Chapter 14 .6

Angle of rotation: The angle through which an object rotates is called angle of rotations.

  • A half-turn means rotation by 180°.
  • A quarter-turn means rotations by 90°.
  • A complete-turn means rotation by 360°.

Order of rotational symmetry: If x° be the smallest angle through which a figure can rotate and still looks the same, then the order of rotational symmetry \(=\left(\frac{360}{x}\right)\)
For example:
(i) Order of square \( =\frac{360}{90}=4\)
(ii) Order of equilateral triangle \( =\frac{360}{90}=6\)

 

Exponents and Powers Class 7 Notes Maths Chapter 13

Exponents and Powers Class 7 NotesOn this page, you will find Exponents and Powers Class 7 Notes Maths Chapter 13 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 13 Exponents and Powers will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 9 Notes Exponents and Powers

Exponents and Powers Class 7 Notes Conceptual Facts

1. Exponents are used to express the large numbers in shorter form to make them easier to read, compare the understand.

2. When a number is multiplied by itself several times, it can be expressed in short form as under

x x x x x x x x x = x5 which is called exponential expression.
x is called base and 5 is exponent or power or index.

3. In general an = a x a x a x a x … n times = an

4. Properties of exponents:

5. Any number raised to power 1 gives the same number.

6. For example: 51 = 5, 1001 = 100

7. A negative number raised to an odd positive integer is always negative.
For example: (-4)3 = (-4) x (-4) x (-4) = -64

8. A negative number raised to an even positive integer is always positive.
For example: (-3)4 = (-3) x (-3) x (-3) x (-3) = 81

9. A positive number raised to an even or odd integer is always positive.
For example:
24 = 2 x 2 x 2 x 2 = 16
= 33 x 3 x 3 = 27

10. Any number raised to power zero, it gives 1.
For example: (-5)° = 1, (1000)°= 1

11. Power 2 is also called square of.

12. Power 3 is also called cube of.

13. Laws of exponents: For any non-zero integers a and b and whole numbers m and
Exponents and Powers Class 7 Notes Maths Chapter 13

 

Comparing Quantities Class 7 Notes Maths Chapter 8

Comparing Quantities Class 7 NotesOn this page, you will find Comparing Quantities Class 7 Notes Maths Chapter 8 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 8 Comparing Quantities will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 8 Notes Comparing Quantities

Comparing Quantities Class 7 Notes Conceptual Facts

1. Ratio: Comparison of two quantities of same kind and with same unit is called ratio.
For example: a : b or \(\frac{a}{b}\) where a is called Antecedent and b Consequent. b

2. Ratio in simplest form: A ratio is said to be in simplest form if its antecedent and consequent have no common factor other than.
For example: \(\frac{2}{3}, \frac{3}{7}, \frac{2}{5}, \frac{6}{7}\) etc. or 2 : 3, 3 : 7, 2 : 5 and 6 : 7 etc.

3. Equivalent ratios: Two ratios can be compared by converting then into like fractions. If the two factions are equal, then they are called as equivalent ratio.
For example: 15 : 20 is equivalent to 3 : 4.
Check whether 1: 2 and 2 : 5 are equivalent.
Comparing Quantities Class 7 Notes Maths Chapter 8
∴ 1 : 2 and 2 : 5 are not equivalent ratios.

4. Comparison of ratios: Let us take from two ratios 2 : 3 and 4 : 5
2 : 3 = \(\frac{2}{3}\) and 4 : 5 \(\frac{2}{3}\)
= 2 x 5 and 3 x 4
2 x 5 and 3 x 4 (By Cross-multiplicative)
10 and 12
\(10<12 \Rightarrow \frac{2}{3}<\frac{4}{5}\)
Hence 2:3< 4:5
We can also compare more than two ratios.

5. Percentage: Ratios can also be compared by converting it into percent i.e. per hundred.
For example:
Let us take two ratios \(\frac{4}{5} \text { and } \frac{3}{4}\) converting into Percentage, we have
Comparing Quantities Class 7 Notes Maths Chapter 8.1

6. Proportion: When two ratios are equivalent, then the four quantities are in proportion.
Let a : b and c : d are equivalent ratios
a : b :: c : d      [:: Symbol of proportion]
\(\frac{a}{b}=\frac{c}{d}\) ⇒ a x d = c x b
a and d are called extremes and b and c are called means
∴ Product of extremes = Product of means

7. Continued proportion: If a, b and c be three quantities such that a: b:: b: c, then a, b, c are in continued proportion.
\(\frac{a}{b}=\frac{b}{c} \quad \Rightarrow \quad b^{2}=a c \Rightarrow b=\sqrt{a c}\)

8. Unitary method: In this method, we find the value of unit quantity and then the value of required quantity is calculated. There are two types of variation.

  • Direction variation
  • Inverse variation

9. Conversion of a fraction into percent: To convert \(\frac{2}{5}\) into percent, we have
\(\frac{2}{5}\) x 100% =40%

10. Conversion of percent into fraction: To convert 20% into fraction, we have
20% = \(\frac{20}{100}=\frac{1}{5}\)

11. Conversion of a ratio into per cent: To convert 4 : 5 into per cent, we have
4:5= \(\frac{4}{5}\) x 100% = 80%

12. Conversion of a percent into ratio: To convert 75% into ratio, we have
75% = \(\frac{75}{100}=\frac{3}{4}\) i.e, 3:4

13. Simple interest:
Comparing Quantities Class 7 Notes Maths Chapter 8.2
[Here SP means selling price and CP means cost price]

Comparing Quantities Class 7 Notes Maths Chapter 8.3
Profit and Loss per cent are always calculated on CP.

Congruence of Triangles Class 7 Notes Maths Chapter 7

Congruence of Triangles Class 7 NotesOn this page, you will find Congruence of Triangles Class 7 Notes Maths Chapter 7 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 7 Congruence of Triangles will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 7 Notes Congruence of Triangles

Congruence of Triangles Class 7 Notes Conceptual Facts

1. Congruence: The objects having same shape and same size are called congruent. The symbol of congruence is ‘≅’.
Example:

  • Two coins of same denominations.
  • Two toys made of the same mould.
  • Two biscuits in the same packet.

2. Congruence of triangles: Two triangles are said to be congruent if all the six elements of one triangle are equal to the corresponding six elements of the other.

Congruence of Triangles Class 7 Notes Maths Chapter 7.2
Example: ΔABC is congruent to ΔPQR
if AB = PQ, BC = QR, AC = PR
and ∠A = ∠P, ∠B = ∠Q and ∠C = ∠R
∴ ΔABC ≅ ΔPQR

3. Congruence of plane figures: Two plane figures are said to be congruent if each superposed on the other i.e., covers each other properly.
Examples:

  • Leaves of the same branch.
  • Two squares with same length of sides.
  • Two circles with same radii.

Congruence of Triangles Class 7 Notes Maths Chapter 7.3

4. Congruence of line segments:
Two line segments are said to be congruent if they have equal lengths.
Congruence of Triangles Class 7 Notes Maths Chapter 7.4
Example:
∵ \(\overline{\mathrm{PQ}}=\overline{\mathrm{RS}}\) = 6.5 cm
∴ \(\overline{\mathrm{PQ}} \cong \overline{\mathrm{RS}}\)

5. Congruence of angles:
Two angles are said to be congruent if they have the same degree measure.
Congruence of Triangles Class 7 Notes Maths Chapter 7.5
Example:
∠AOB = 60° and ∠PQR = 60°
∴ ∠AOB ≅ ∠PQR [means superpose]
ar m ∠AOB = m∠PQR

Conditions for congruence of triangles:

1. Side-Side-Side (SSS): If three sides of one triangle are respectively equal the corresponding sides of the other triangle, then the two triangles are congruent by SSS criterion.
Congruence of Triangles Class 7 Notes Maths Chapter 7.6
In ΔABC and ΔDEF, we have
AB = DE = 3 cm
BC = EF = 4 cm and
AC = DF = 5 cm
∴ ΔABC ≅ ΔDEF (By SSS criterion)

2. Side-Angle-Side (SAS): If two sides and the included angle of one triangle are respectively equal to the corresponding two sides and their included angle, then the two triangles are congruent (by SAS criterion).
Congruence of Triangles Class 7 Notes Maths Chapter 7.7
In ΔABC and ΔPQR,
we have AB = PQ BC = QR
and ∠B = ∠Q
∴ ΔABC ≅ ΔPQR

3. Angle-Side-Angle (ASA): If two angles and the included side of one triangle are respectively equal to the corresponding two angles and the included side, then the triangles are congruent (by ASA criterion).
Congruence of Triangles Class 7 Notes Maths Chapter 7.8
In ΔPQR and ΔSTU, we have
∠Q = ∠T and ∠R = ∠U
QR = TU
∴ ΔPQR ≅ ΔSTU (by ASA criterion)

4. Right-Angle-Hypotenuse-Side (RHS): If the right angle, hypotenuse and one side of one triangle
are respectively equal to the corresponding right angle, hypotenuse and side of the other triangle, then the two triangles are congruent m (by RHS).

Congruence of Triangles Class 7 Notes Maths Chapter 7.9
In ΔPQR and ΔSTU,
we have PQ = ST
hypt. PR = hypt. SU
∠Q = ∠T = 90°
∴ ΔPQR ≅ ΔSTU

The Triangles and its Properties Class 7 Notes Maths Chapter 6

The Triangles and its Properties Class 7 NotesOn this page, you will find The Triangles and its Properties Class 7 Notes Maths Chapter 6 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 6 The Triangles and its Properties will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 6 Notes The Triangles and its Properties

The Triangles and its Properties Class 7 Notes Conceptual Facts

1. A triangle is a simple closed figure made up of three line segments.

2. ΔABC has three sides AB, BC and CA and three angles ∠ABC, ∠BCA and ∠CAB. These are called six elements of the triangle.
The Triangles and its Properties Class 7 Notes Maths Chapter 6
3. Scalene triangle: If all sides of the triangle are unequal, then it is called scalene triangle.
AB ≠ BC ≠ CA
The Triangles and its Properties Class 7 Notes Maths Chapter 6.1
4. Isosceles triangle: A triangle in which any two sides are equal is called isosceles triangle. Angle opposite to equal sides are also equal to each other.
In ΔABC, AB = AC and ∠ABC = ∠ACB
The Triangles and its Properties Class 7 Notes Maths Chapter 6.2

5. Equilateral triangle: A triangle in which all sides are of equal length is called equilateral triangle. Each angle is equal to 60°. In ΔABC, AB = BC = AC and ∠A = ∠B = ∠C
The Triangles and its Properties Class 7 Notes Maths Chapter 6.3

6. Acute angled triangle: A triangle having all angles less than 90° is called acute angled triangle.
In ΔABC, ∠A = ∠90°, ∠B = ∠90° and ∠C = ∠90°.
The Triangles and its Properties Class 7 Notes Maths Chapter 6.4
7. Obtuse angled triangle: A triangle having one of its three angles is more than 90° is called obtuse angled triangle.
In ΔABC, ∠ABC > 90°
The Triangles and its Properties Class 7 Notes Maths Chapter 6.5
8. Right angled triangle: A triangle having its one angle equal to 90° is called right angled triangle.
In ΔABC, ∠B – 90°
The Triangles and its Properties Class 7 Notes Maths Chapter 6.6

9. Pythagoras properties: In a right angled triangle, the square of the hypotenuse is equal to the sum of the square of the other sides. In ΔPQR, ∠Q = 90° and PR2 = PQ2 + QR2
The Triangles and its Properties Class 7 Notes Maths Chapter 6.7

10. Median of a triangle: Line segment joining a vertex to the mid-point of its opposite side in a triangle is called the median of the triangle.
In ΔABC, D is the mid-point of BC and AD is the median.
The Triangles and its Properties Class 7 Notes Maths Chapter 6.8

11. Altitude of a triangle: Perpendicular drawn from any vertex to the opposite side of a triangle is called its altitude.

Perimeter and Area Class 7 Notes Maths Chapter 11

Perimeter and Area Class 7 NotesOn this page, you will find Perimeter and Area Class 7 Notes Maths Chapter 11 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 11 Perimeter and Area will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 11 Notes Perimeter and Area

Perimeter and Area Class 7 Notes Conceptual Facts

1. Perimeter is the actual distance around a closed figure.

2. Perimeter of a regular polygon = Number of sides x Length of one side

3. Perimeter of a square = 4 x side

Perimeter and Area Class 7 Notes Maths Chapter 11

4. Perimeter of a triangle = AB + BC + CA (Sum of all sides of triangle)

Perimeter and Area Class 7 Notes Maths Chapter 11.1

5. Perimeter of a rectangle = 2 [length + breadth]
= 2(l+ b)

Perimeter and Area Class 7 Notes Maths Chapter 11.2

6. Circumference of a circle is the actual distance around it.

7. Ratio of the circumference and the diameter of a circle is a constant

8. The numerical value of π is taken as \(\frac{22}{7}\) or 3.14. (approximate)

Perimeter and Area Class 7 Notes Maths Chapter 11.3
9. Circumference of a circle = 2πr, where r is the radius of the circle.

10. Area of a rectangle = length x breadth = l x b

Perimeter and Area Class 7 Notes Maths Chapter 11.4

11. Area of a triangle = \(\frac{1}{2}\) x base x height = \(\frac{1}{2}\) x b x h

Perimeter and Area Class 7 Notes Maths Chapter 11.5

12. Area of circle = πr2, where r is the radius of the circle.

Perimeter and Area Class 7 Notes Maths Chapter 11.6

13. Area of a parallelogram = base x height

Perimeter and Area Class 7 Notes Maths Chapter 11.7

14. Area of a square = (Side)2 = l2

Perimeter and Area Class 7 Notes Maths Chapter 11.8

Conversion of units

Perimeter and Area Class 7 Notes Maths Chapter 11.9

Lines and Angles Class 7 Notes Maths Chapter 5

Lines and Angles Class 7 NotesOn this page, you will find Lines and Angles Class 7 Notes Maths Chapter 5 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 5 Lines and Angles will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 5 Notes Lines and Angles

Lines and Angles Class 7 Notes Conceptual Facts

1. Line: A line is a perfectly straight figure extended for ever in both directions.
Example :
Lines and Angles Class 7 Notes Maths Chapter 5 .1

represent by \(\stackrel{\leftrightarrow}{A B}\)

2. Line segment: The shortest distance between any two point is called line segment. It has no end points.
Example :
Lines and Angles Class 7 Notes Maths Chapter 5. 2

represent by \(\overline{\mathrm{PQ}}\)

3. Ray: A line segment extended to one direction only is called a ray. It has one initial point and no definite length.
Example :
Lines and Angles Class 7 Notes Maths Chapter 5. 3
represent by \(\overrightarrow{\mathrm{OP}}\)

4. Angle: An angle is formed when two lines or line segments meet or intersect each other.
OR
Two rays having same initial point form an angle.
Example :

Lines and Angles Class 7 Notes Maths Chapter 5. 4

Type of angles:
(i) Acute angle: An angle whose measure is more than 0° and less than 90° is called an acute angle.
Example:
Lines and Angles Class 7 Notes Maths Chapter 5. 5

(ii) Obtuse angle: An angle whose measure is more than 90° and less than 180° is called obtuse angle.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 6

(iii) Right angle: An angle whose measure is 90° is called right angle.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 7

(iv) Straight angle: An angle whose measure is 180° is called straight angle.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 8

(v) Reflex angle: An angle whose measure is more than 180° but less than 360° is called reflex angle.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 9

Pair of angles:
(i) Adjacent angles: Two angles having a common aim and a common vertex and non-common arms he on either side of the common arm are called adjacent angles.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 10

(ii) Complementary angles: Any two angles whose sum is 90° are called complementary angles.
Example:
Lines and Angles Class 7 Notes Maths Chapter 5. 11
∠AOB = 60° and ∠PQR = 300
∠AOB + ∠PQR = 60° + 30° = 90°
∴ ∠AOB and ∠PQR are complementary angles.

(iii) Supplementary angles: Any two angles whose sum is 180° are called supplementary angles.
∠AOB and ∠PQR are supplementary angles.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 12

(iv) Linear pair of angles: When the sum of two adjacent angles is 180°, then they are called linear pairs.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 13

(v) Vertically opposite angles: When two lines intersect each other, they form a pair of angles opposite to each other.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 14

∠AOD and ∠COB) and (∠AOC and ∠BOD) are the pairs of vertically opposite angles.
Vertically opposite angles are always equal to each other, i.e., ∠AOD = ∠COB and ∠AOC = ∠BOD

Pairs of Lines:
(i) Intersecting Lines: The two lines are said to be intersecting lines if they have a common point which is known as point of intersection.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 15

\(\stackrel{\leftrightarrow}{\mathrm{AB}} \text { and } \stackrel{\leftrightarrow}{\mathrm{CB}}\) are intersecting lines having common point O.

(ii) Parallel lines: Two lines are said to be parallel if they do not intersect each other even on extended in either direction.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 16

\(\stackrel{\leftrightarrow}{\mathrm{PQ}} \text { and } \stackrel{\leftrightarrow}{\mathrm{AB}} \) are parallel to each other and represented as \(\stackrel{\leftrightarrow}{P Q} \| \stackrel{\leftrightarrow}{A B}\).

Transversal: When a line intersect two or more lines in a plane at distinct points it is called as transversal.
Example:

Lines and Angles Class 7 Notes Maths Chapter 5. 17

m is the transversal intersecting two line \(\stackrel{\leftrightarrow}{A B} \text { and } \stackrel{\leftrightarrow}{C D}\) at n and o respectively.

Angles made by transversal
Here \(l_{1} \| l_{2}\) and t is the transversal line.

Lines and Angles Class 7 Notes Maths Chapter 5. 18

Types of angles Angles represented by
Interior ∠3, ∠4, ∠5, ∠6
Exterior ∠1, ∠2, ∠7, ∠8
Alternate interior (∠3 and ∠6), (∠4 and ∠5)
Alternate exterior (∠1 and ∠8), (Z2 and Z7)
Corresponding (∠3 and ∠7), (∠1 and ∠5), (∠2 and ∠6),
(∠4 and ∠8)
Interior on the same side of the transversal (∠3 and ∠5), (∠4 and ∠6)

Properties:
(i) Vertically opposite angles are equal.
∠1 = ∠4, ∠2 = ∠3,
∠5 = ∠8, ∠6 = ∠7

(ii) Alternate interior angles are equal.
∠3 = ∠6 and ∠4 = ∠5

(iii) Alternate exterior angles are equal.
∠1 = ∠8 and ∠2 = ∠7

Lines and Angles Class 7 Notes Maths Chapter 5. 19
(iv) Corresponding angles are equal.
∠1 = ∠5, ∠2 = ∠6,
∠3 = ∠7, ∠4 = ∠8

(v) Sum of interior angle on the same sides of transversal is 180°.
∠3 + ∠5 = 180°, ∠4 + ∠6 =180°

(vi) Linear pairs are supplementary angles.
∠1 + ∠3 = 180°, ∠1 + ∠2 = 180°
∠2 + ∠4 = 180°, ∠3 + ∠4 = 180°
∠5 + ∠6 = 180°, ∠6 + ∠8 = 180°
∠7 + ∠8 = 180°, ∠5 + ∠7 = 180°

Data Handling Class 7 Notes Maths Chapter 3

Data Handling Class 7 NotesOn this page, you will find Data Handling Class 7 Notes Maths Chapter 3 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 3 Data Handling will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 3 Notes Data Handling

Data Handling Class 7 Notes Conceptual Facts

1. Data: The collection of informations in the form of numerical figures is called data.
Each number in a data is called observation or variate and number of times a particular observation occurs is called its frequency.

2. Range: The difference between the highest and the lowest observation in a given data is called ‘Range’.

3. Frequency distribution table: A table representing the frequency of various observations is called frequency distribution table.

4. Mean, Average or Arithmetic Mean:
\(\text { Mean }=\frac{\text { Sum of all observations }}{\text { Number of observations }}=\frac{\Sigma x_{i}}{\Sigma f_{i}}\) where i=1,2,3,…………

Mean of grouped data \(=\frac{\Sigma f_{i} x_{i}}{\Sigma f_{i}}\) i=1,2,3,…………

5. Median: When the observations are arranged in ascending or descending order, then the middle observation is called its Median.
Data Handling Class 7 Notes Maths Chapter 3

6. Mode: The observation which occurs maximum number of times in a given data is called its ‘mode’. Mean, median
and mode are called measures of central tendency.

7. Bar graph: The representation of data in the form of bars of uniform width is called bar graph.

8. A double bar graph is used to compare the information related to two types of data.

9. Probability is a chance of happening and not happening and event.

10. The probability of an event which is certain to happen is 1. It is also called as ‘sure event’.

11. The probability of an event which is impossible to happen is 0. It is also called as ‘impossible event’.

Practical Geometry Class 7 Notes Maths Chapter 10

On this page, you will find Practical Geometry Class 7 Notes Maths Chapter 10 Pdf free download. CBSE NCERT Class 7 Maths Notes Chapter 10 Practical Geometry will seemingly help them to revise the important concepts in less time.

CBSE Class 7 Maths Chapter 10 Notes Practical Geometry

Practical Geometry Class 7 Notes Conceptual Facts

1. By using properties of a transversal and parallel lines, a line parallel to a given line passing through a given point lying not on the line can be drawn.
Let P is any point outside of the given line T. P is joined to any point Q on the line T.
Join P and Q. Draw an angle 2 equal to angle 1. We get m || l.

2. We can draw a triangle if any one of the following conditions are given:

  • Three sides (By SSS criterion)
  • Two sides and the angle between them (By SAS criterion)
  • Two angles and the side included between them (By ASA criterion)
  • The hypotenuse and a leg of a right-angled triangle (By RHS criterion)

Practical Geometry Class 7 Notes Maths Chapter 10