Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 ↓


Geometry


Geometry, in its simplest form, is the branch of mathematics that deals with the size, shape, and position of objects. In Class 6, you will explore the basic ideas and terms of geometry, learn to recognize shapes, and understand their properties and relationships.

Basic terms and definitions

Let's start with some basic terms that are frequently used in geometry. Understanding these terms will help you understand more complex concepts later.

  • Point: A point indicates a location in space. It has no size, no width, no length and no depth. It is just a position. A point is usually designated with a capital letter, such as A.
  • Line: A line is a straight path that extends in two opposite directions without ending. It has no thickness and is usually drawn with arrows at both ends.
  • Line segment: A line segment is a portion of a line that consists of two end points and all the points between them. If you have points A and B, the line segment would be named segment AB.
  • Ray: A ray is a part of a line that starts from a point and extends endlessly in one direction. It has an end point.
  • Plane: A plane is a flat surface that extends in all directions without end. Planes are two-dimensional, having length and width, but no thickness.
  • Angle: An angle is formed by two rays that have the same end point. The rays are the sides of the angle and the common end point is the vertex of the angle.

Types of lines

It is important to understand the different types of lines in geometry, as they form the basis of geometric shapes.

Horizontal line: A line that runs from left to right or right to left.
Vertical line: A line that goes from top to bottom or bottom to top.
Parallel lines: Lines in a plane that do not meet; they are always the same distance apart.
Perpendicular lines: Lines that meet or cross each other and form right angles.

Types of angles

Angles are an essential part of geometry. Here are the different types of angles you'll encounter:

Acute angle: An angle that is less than 90 degrees.
Right angle: An angle that is exactly 90 degrees.
Obtuse angle: An angle that is more than 90 degrees but less than 180 degrees.
Straight angle: An angle that is exactly 180 degrees.
Reflex angle: An angle that is greater than 180 degrees.

Measuring angles

Protractors are used to measure angles in degrees. There are 360 degrees in a full circle.

90°

Polygon

Polygons are flat shapes with straight sides. They can have any number of sides, but in 6th grade you will focus on:

Triangle: A polygon with three sides.
Quadrilateral: A polygon with four sides.
Pentagon: A polygon with five sides.
Hexagon: A polygon with six sides.
Heptagon: A polygon with seven sides.
Octagon: A polygon with eight sides.

Triangle

There are three types of triangles depending on the length of the sides:

Equilateral triangle: All sides are of equal length.
Isosceles triangle: Two sides are of equal length.
Scalene triangle: All sides are of different lengths.

Triangles can also be classified based on their angles:

Acute triangle: All angles are less than 90 degrees.
Right triangle: One angle is exactly 90 degrees.
Obtuse-angled triangle: These have one angle more than 90 degrees.
60° 60° 60°

Quadrilateral

A quadrilateral has four sides and can be of different types depending on its properties:

Rectangle: Opposite sides are equal, and each angle is 90 degrees.
Square: All four sides are equal, and each angle is 90 degrees.
Parallelogram: Opposite sides are parallel and of equal length, opposite angles are equal.
Rhombus: All sides are equal, opposite angles are equal.
Trapezoid (US) / Trapezium (UK): At least one pair of parallel sides.
90°

Symmetry

Symmetry in geometry refers to the balance or similarity between two parts of a shape.

  • Line symmetry: If a figure can be divided into two equal parts by a straight line then it has line symmetry.
  • Rotational symmetry: If a figure looks the same even after rotating a certain amount then it has rotational symmetry.

Perimeter and area

Perimeter is the distance around a shape, and area is the space inside a shape.

Circumference

To calculate the perimeter, add up the lengths of all sides:

Perimeter of triangle = side1 + side2 + side3
Perimeter of rectangle = 2 * (length + width)
Perimeter of square = 4 * side

Area

Use these formulas to calculate the area:

Area of a rectangle = length * width
Area of a square = side * side = side²
Area of triangle = (base * height) / 2
Length = 150 Width = 75

3D shapes

When you move beyond flat shapes, you enter the world of three-dimensional (3D) shapes, which have depth in addition to length and width.

  • Cuboid: A 3D shape with six rectangular faces.
  • Cube: A special type of cuboid in which all six faces are squares.
  • Sphere: A circular 3D shape where every point on the surface is the same distance from the center.
  • Cylinder: A 3D shape consisting of two parallel circular bases connected by a curved surface.
  • Cone: A 3D shape with a circular base and a vertex.
  • Pyramid: A 3D shape with a polygonal base and triangular surfaces that meet at a point called the vertex.

Conclusion

Geometry is all around us - in the shapes of buildings, in art, and even in nature. Understanding the basics of geometry helps us see the world in a more structured way. As you continue to explore geometry, you will begin to see patterns and relationships between different shapes, enriching your understanding of both mathematics and the world around you.


Grade 6 → 4


U
username
0%
completed in Grade 6

← Prev (3.3.4)
Simple Interest Calculations in Percentages in Ratio and Proportion
Next (4.1) →
Basic Geometric Shapes

Comments 



Geometry

https://www.buddymath.com/g6/4?bmal=en