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# CBSE - Class 07 - Mathematics - The Triangle and its Properties - NCERT Solutions

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# NCERT solutions for class 7 Mathematics The Triangles and its Properties

## NCERT 7 Mathematics Text book Solutions

### NCERT Class 7 Mathematics Chapter-wise Solutions

• Chapter 1 – Integers
• Chapter 2 – Fractions and Decimals
• Chapter 3 – Data Handling
• Chapter 4 – Simple Equations
• Chapter 5 – Lines and Angles
• Chapter 6 – Practical Geometry
• Chapter 7 – The Triangle and its Properties
• Chapter 8 – Congruence of triangles
• Chapter 9 – Comparing Quantities
• Chapter 10 – Rational numbers
• Chapter 11 – Perimeter and Area
• Chapter 12 – Algebraic Expressions
• Chapter 13 – Exponents and Powers
• Chapter 14 – Symmetry
• Chapter 15 – Visualizing Solid Shapes

Here is the list of topics covered under each chapter of class 7 Mathematics NCERT text book.

### CHAPTER ONE INTEGERS

• 1.1 Multiplication and Division of Integers
• 1.2 Properties of Integers
• 1.3 Properties of multiplication of integers
• 1.4 Word problems including integers

### CHAPTER TWO FRACTIONS AND DECIMALS

• 2.1 Let’s recal fractions
• 2.2 Multiplication of Fractions (fraction x whole number & fractionx fraction)
• 2.3 Division of fractions (whole number/fraction; reciprocal of a fraction; fraction/whole number; fraction/fraction)
• 2.4 How Well have you learnt about decimal numbers
• 2.5 Multiplication & Division of Decimal Numbers (decimal x decimal; decimal x whole number; decimal x 10, 100, 1000)
• 2.6 Word Problems on Fractions and Decimal Numbers

### CHAPTER THREE DATA HANDLING

• 3.1 Introduction: Why should we organize data?
• 3.2 Data collection and organizing data
• 3.3 Organisation of Data
• 3.4 Representative Values
• 3.5 Arithmetic Mean & Range
• 3.6 Mode
• 3.7 Median
• 3.8 Use of bar graphs with a Different Purpose
• 3.9 Chance & Probability

### CHAPTER FOUR SIMPLE EQUATIONS

• 4.1 Recall : Expressions and Equations
• 4.2 Setting up an equation
• 4.3 Solving an equation
• 4.4 Tracing Back: from solution to equation
• 4.5 Application of simple equations to practical situations

### CHAPTER FIVE LINES AND ANGLES

• 5.1 Introduction to Lines and Angles
• 5.2 Related Angles: Complementary and supplementary angles
• 5.3 Pairs of Lines : Intersecting Line and Transversal
• 5.4 Check for parallel lines

### CHAPTER SIX THE TRIANGLES AND ITS PROPERTIES

• 6.1 Introduction : Recall the triangles
• 6.2 Medians & Altitudes of a triangle
• 6.3 Exterior Angle of a triangle & its property
• 6.4 Angle sum property of a triangle
• 6.5 Equilateral & Isosceles Triangles
• 6.6 Sum of the length of two sides of a triangle
• 6.7 Right-Angled Triangles and Pythagoras Property

### CHAPTER SEVEN CONGRUENCE OF TRIANGLES

• 7.1 The idea of congruence in geometry
• 7.2 Congruence of plane figures, line segments, angles
• 7.3 Criteria for congruence of triangles
• 7.4 Congruence among right-angled triangles

### CHAPTER EIGHT COMPARING QUANTITIES

• 8.1 Comparing Quantities
• 8.2 Equivalent Ratios
• 8.3 Percentage : Another way of comparing quantities
• 8.4 Converting fractional and decimal numbers to percentage
• 8.5 Converting percentage to fractions or decimal numbers
• 8.6 Uses of Percentage : Interpreting and converting percentages
• 8.7 Uses of Percentage : Ratio to Percent, Increase of Decrease as percent
• 8.8 Profit or Loss as Percentage
• 8.9 Introduction to simple interest for one and multiple years

### CHAPTER NINE RATIONAL NUMBERS

• 9.1 Introduction to rational numbers and their need
• 9.2 Positive and negative natural numbers and their representation on number line
• 9.3 Rational numbers in standard form
• 9.4 Representation of rational number as a decimal
• 9.5 Comparison of rational numbers
• 9.6 Rational numbers between two rational numbers
• 9.7 Operations in rational numbers
• 9.8 Word problems on rational numbers (all operations)

### CHAPTER TEN PRACTICAL GEOMETRY

• 10.1 Construction of a line parallel to a given line, through a point not on the line
• 10.2 Construction of Triangles : An idea
• 10.3 Constructing a triangle when the lengh of its sides are known (SSS Criterion)
• 10.4 Constructing a triangle when the length its two sides and the measure of the angle between them are known (SAS Criterion)
• 10.5 Constructing a triangle when the measure of two of its angles and the length of the side included between them is given (ASA Criterion)
• 10.6 Constructing a Right-Angled Triangle when the length of one leg and its Hypotenous are given (RHS Criterion)

### CHAPTER ELEVEN PERIMETER AND AREA

• 11.1 Triangles
• 11.2 Area of a parallelogram & triangle
• 11.3 Circles : Circumference & Area
• 11.4 Perimeter of Polygons
• 11.5 Conversion of units and its applications

### CHAPTER TWELVE ALGEBRAIC EXPRESSIONS

• 12.1 Introduction: Formation of an equation
• 12.2 Terms of an expression : Factors and coefficients of a term
• 12.3 Like and unlike terms : Monomials, Binomials, Trinomials and Polynomials
• 12.4 Addition and subtraction of algebraic expressions
• 12.5 Finding the value of an expression
• 12.6 Using algebraic expression – formulas and rules [Perimeter formula; area formula]
• 12.7 Simple linear equations
• 12.8 Patterns in numbers and geometry

### CHAPTER THIRTEEN EXPONENTS AND POWERS

• 13.1 Why exponents and powers
• 13.2 Exponents: The shorthand for repeated multiplications
• 13.3 Laws of exponents
• 13.4 Decimal number system and expressing large numbers in the standard form

### CHAPTER FOURTEEN SYMMETRY

• 14.1 Recalling reflection symmetry
• 14.2 Line Symmetry
• 14.3 Rotational Symmetry
• 14.4 A comparison between line symmetry and rotational symmetry

### CHAPTER FIFTEEN VISUALIZING SOLID SHAPES

• 15.1 Introduction to plane figures and solid shapes (faces, edges and vertices)
• 15.2 Building 3-D Shapes
• 15.3 Oblique Sketches
• 15.4 Isometric Sketches
• 15.5 Different sections of a solid (slicing/cutting & shadows)

## NCERT Solutions for Class 7th Mathematics

We have learnt about whole numbers and integers in Class VII. We know that integers form a bigger collection of numbers which contains whole numbers and negative numbers. What other differences do you find between whole numbers and integers? In this chapter, we will study more about integers, their properties and operations. First of all, we will review and revise what we have done about integers in previous class.

## NCERT Solutions Chapter 06:The Triangle And Its Properties

A triangle, you have seen, is a simple closed curve made of three line segments. It has three vertices,three sides and three angles. The side opposite to the vertex A is BC. Can you name the angle opposite to the side AB? You know how to classify triangles based on the (i)sides (ii)angles.

• (i)Based on Sides:Scalene,Isosceles and Equilateral triangles.
• (ii)Based on Angles:Acute-angled,Obtuse-angled and Right-angled triangles.

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