Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 ↓


Geometry


Geometry is a branch of mathematics that studies the size, shape, position, angles, and dimensions of objects. It is one of the oldest sciences and has existed since ancient times to help humans in many activities like building houses, measuring land, etc. In class 7, geometry involves learning about different shapes, understanding their properties, and finding things like area, perimeter, and volume using mathematical calculations.

Basic shapes

Geometry begins with understanding the basic shapes. Let's take a look at some of these shapes:

Point

A point represents a precise position or location. It has no length, width, or height. It is just a dot on the paper. We usually name points with capital letters like A, B, or C.

Line

A line is a straight path that extends forever in both directions. A line has no end points. It is designated by any two points on the line. For example, if a line passes through points A and B, we call it (overleftrightarrow{AB}).

    
        
        A
        B

Line segment

A line segment is a part of a line that has two end points. The difference between a line and a line segment is that a line always continues in both directions, but a line segment has end points and break points. If a segment has end points A and B, we write it as (overline{AB}).

    
        
        
        
        A
        B

Ray

A ray is a part of a line that has one end point and extends endlessly in one direction. It starts from one point and continues forever in the same direction. If a ray starts from point A and passes through point B, we call it (overrightarrow{AB}).

    
        
        
        A
        B

Angles

An angle is formed when two rays meet at a common end point called the vertex. Angles are measured in degrees. There are different types of angles:

  • Acute angle: An angle less than 90 degrees.
    
        
        
        A
        B
        C
  • Right angle: An angle that is exactly 90 degrees.
    
        
        
        A
        B
        C
  • Obtuse angle: An angle greater than 90 degrees but less than 180 degrees.
    
        
        
        A
        B
        C

Types of triangles

Triangles are shapes with three sides and three angles. They are one of the simplest polygons. Here are some common types of triangles:

  • Equilateral triangle: All sides are the same length, and all angles are equal to 60 degrees.
  • Isosceles triangle: It has two sides of equal length and two equal angles.
  • Scalene triangle: All sides and angles are different.

Quadrilateral

Quadrilaterals are polygons with four sides. The sum of all the interior angles of a quadrilateral is always 360 degrees. Let us learn about some common quadrilaterals:

  • Square: All sides are equal, and all angles are 90 degrees.
  • Rectangle: Opposite sides are equal, and all angles are 90 degrees.
  • Parallelogram: Opposite sides are equal and parallel, but the angles are not 90 degrees.
  • Rhombus: All sides are equal, and opposite angles are also equal.
  • Trapezoid: It has only one pair of opposite sides parallel.

Circumference

The perimeter is the distance around a shape. To find the perimeter, you add up the lengths of all the sides. Here are some examples:

Perimeter of a square

    Formula: P = 4a
    Where 'a' is the length of the side.
    Example: If one side of a square is 5 cm, then the perimeter will be:
    P = 4 × 5 = 20 cm
    P = 4 × 5 = 20 cm

Perimeter of a rectangle

    Formula: P = 2(l + w)
    Where 'l' is the length and 'w' is the width.
    Example: If the length of a rectangle is 8 cm and width is 3 cm, then the perimeter will be:
    P = 2(8 + 3) = 2 × 11 = 22 cm
    P = 2(8 + 3) = 2 × 11 = 22 cm

Area

Area is the amount of space inside a shape. It is measured in square units such as square meters or square inches. Here are some formulas to find the area of different shapes:

Area of a square

    Formula: A = a²
    Where 'a' is the length of the side.
    Example: If one side of a square is 4 cm, then its area will be:
    A = 4 × 4 = 16 cm²
    A = 4 × 4 = 16 cm²

Area of a rectangle

    Formula: A = l × w
    Where 'l' is the length and 'w' is the width.
    Example: If the length of a rectangle is 10 cm and width is 5 cm, then the area will be:
    A = 10 × 5 = 50 cm²
    A = 10 × 5 = 50 cm²

Area of a triangle

    Formula: A = ½ × base × height
    Example: If the base of a triangle is 6 cm and height is 3 cm, then the area is:
    A = ½ × 6 × 3 = 9 cm²
    A = ½ × 6 × 3 = 9 cm²

Volume

Volume is the amount of space inside a 3D object. It is measured in cubic units such as cubic meters or cubic inches. Here are formulas to find the volume of some commonly studied 3D shapes:

Volume of a cube

    Formula: V = a³
    Where 'a' is the length of the side.
    Example: If one side of a cube is 3 cm, then the volume will be:
    V = 3 × 3 × 3 = 27 cm³
    V = 3 × 3 × 3 = 27 cm³

Volume of a rectangular prism (box)

    Formula: V = l × w × h
    Where 'l' is the length, 'w' is the width, and 'h' is the height.
    Example: If the length of a box is 5 cm, width 4 cm and height 3 cm, then the volume will be:
    V = 5 × 4 × 3 = 60 cm³
    V = 5 × 4 × 3 = 60 cm³

Circles

A circle is a simple figure consisting of all the points in a plane that are equidistant from a given point called the center. Here are some key terms and formulas related to circles:

Circumference

The circumference of a circle is the distance around the circle. This is just like the perimeter, but for circles.

    Formula: C = 2πr
    Where 'r' is the radius.
    Example: If the radius of a circle is 7 cm, then the circumference will be:
    C = 2 × π × 7 ≈ 44 cm
    C = 2 × π × 7 ≈ 44 cm

Area of a circle

    Formula: A = πr²
    Where 'r' is the radius.
    Example: If the radius of a circle is 5 cm, then the area will be:
    A = π × 5 × 5 ≈ 78.5 cm²
    A = π × 5 × 5 ≈ 78.5 cm²

Remember, the π (pi) in these formulas is approximately 3.14, which is a mathematical constant.

Conclusion

Geometry is all about shapes and spaces. It teaches us to measure length, angles, perimeter, area, and volume of various shapes. Understanding these concepts can help you see the world in a different way, whether it's calculating the paint needed to cover a wall, determining how much soil is needed to fill a garden bed, or even designing buildings.

Always look for connections to the real world when studying geometry. Geometry is all around us, and it gives us a way to understand the shapes and spaces we encounter every day. Keep practicing, keep exploring, and keep asking questions, and you will build a strong foundation of understanding in geometry.


Grade 7 → 4


U
username
0%
completed in Grade 7

← Prev (3.3.1)
Solving Problems Using the Unitary Method
Next (4.1) →
Lines and Angles

Comments 



Geometry

https://www.buddymath.com/g7/4?bmal=en