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 → Triangles ↓


Properties of Triangles


A triangle is a simple closed figure made up of three line segments. It is one of the basic shapes in geometry. Understanding the properties of triangles is essential as it lays the foundation for learning more complex geometric concepts. In this lesson, we will explore the various properties of triangles in detail.

Basic properties of triangles

1. The sum of the angles of a triangle

A fundamental property is that the sum of the interior angles in a triangle is always 180 degrees. This can be expressed as:

angle A + angle B + angle C = 180°

This rule applies to all triangles, regardless of their type. For example, consider a triangle with angles of 50°, 60°, and 70°. If you add them together you get:

50° + 60° + 70° = 180°

2. Types of triangles based on angles

Let us look at the different types of triangles based on the angles.

Acute triangle

An acute-angled triangle is a triangle whose all three angles are less than 90 degrees.

ABCAll angles < 90°

Right triangle

One angle of a right triangle is exactly 90 degrees. The side opposite the right angle is the hypotenuse, and it is the longest side of the triangle.

ABCOne angle = 90°

Obtuse-angled triangle

An obtuse-angled triangle has one angle more than 90 degrees.

ABCAn angle > 90°

3. Types of triangles based on sides

Triangles can also be classified based on the length of their sides.

Equilateral triangle

The three sides of an equilateral triangle are of equal length. Therefore, the three angles are also equal and each measures 60 degrees.

ABCall sides are equal

Isosceles triangle

In an isosceles triangle at least two sides are of equal length. The angles opposite to equal sides are also equal.

ABCtwo sides are equal

Scalene triangle

In a scalene triangle, none of the sides are equal. The three sides are of different lengths and as a result, the three angles are different.

ABCno sides are equal

Other important properties

4. Triangle inequality theorem

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. It can be written as:

a + b > c
a + c > b
b + c > a

where a, b, and c are the lengths of the sides of the triangle. For example, if we have a triangle with sides 5, 7, and 10, it satisfies:

5 + 7 > 10
5 + 10 > 7
7 + 10 > 5

5. Special lines in triangles

There are many special lines associated with triangles as well.

Height

The altitude of a triangle is a line segment from the vertex to the opposite side, forming a right angle (90 degrees) with that side. The altitude is also sometimes called the height of the triangle.

Median

The median of a triangle is a line segment that joins the vertex to the midpoint of the opposite side, and thus divides the opposite side into two equal parts.

Angle bisector

The angle bisector in a triangle is the line that divides an angle into two equal smaller angles.

Perpendicular bisector

The perpendicular bisector is a line that divides a side into two equal parts at a 90 degree angle.

Triangles in daily life

Understanding triangles is not just a matter of classroom learning; it also has practical applications in real life. Here are some examples of how triangles are used everyday:

Architecture

Triangles are often used in architecture to build strong and stable structures. The triangular shape provides better stability to structures such as bridges and buildings.

Engineering

Engineers use triangular structures to evenly distribute weight and maintain balance. This is especially important in the design of various machinery and vehicles.

Art and design

Triangles are commonly seen in art and design. Artists use triangle formations to create symmetry and balance in their compositions.

Guidance

Triangles are also important in navigation, often used in triangulation techniques to find an unknown location using the known positions of two other points.

Conclusion

Understanding the properties of triangles is important for exploring more complex geometric concepts. Whether in math, science, or practical applications in real life, triangles are fundamental shapes that help explain and create the world around us.


Grade 6 → 4.2.2


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Types of Triangles
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Properties of Triangles

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