Grade 5
  1. Number Sense and Place Value  1.1. Understanding Large Numbers  1.2. Place Value up to Millions  1.3. Comparing and Ordering Numbers  1.4. Rounding Whole Numbers  1.5. Expanded Form and Standard Form  1.6. Estimation in Calculations
  2. Operations with Whole Numbers  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Multiplication Concepts and Strategies  2.4. Division Concepts and Strategies  2.5. Multi-Digit Multiplication  2.6. Long Division  2.7. Order of Operations
  3. Fractions  3.1. Introduction to Fractions  3.2. Equivalent Fractions  3.3. Simplifying Fractions  3.4. Comparing and Ordering Fractions  3.5. Addition and Subtraction of Fractions  3.6. Multiplication of Fractions  3.7. Division of Fractions  3.8. Mixed Numbers and Improper Fractions  3.9. Converting Between Improper Fractions and Mixed Numbers
  4. Decimals  4.1. Understanding Decimals  4.2. Place Value in Decimals  4.3. Comparing and Ordering Decimals  4.4. Rounding Decimals  4.5. Addition and Subtraction of Decimals  4.6. Multiplication of Decimals  4.7. Division of Decimals  4.8. Converting Decimals to Fractions and Vice Versa
  5. Measurement  5.1. Length Measurement (Metric and Customary Units)  5.2. Weight and Mass Measurement  5.3. Volume and Capacity Measurement  5.4. Area of Squares and Rectangles  5.5. Perimeter of Polygons  5.6. Time and Elapsed Time  5.7. Temperature  5.8. Understanding Metric Conversions
  6. Geometry  6.1. Types of Lines and Angles  6.2. Measuring Angles  6.3. Classifying Triangles  6.4. Properties of Quadrilaterals  6.5. Symmetry and Reflection  6.6. Transformations (Translation, Rotation, Reflection)  6.7. Coordinate Plane and Plotting Points  6.8. 3D Shapes and Their Properties  6.9. Nets of 3D Shapes  6.10. Understanding Congruence and Similarity
  7. Data and Probability  7.1. Introduction to Data Collection  7.2. Organizing Data (Tables and Tally Charts)  7.3. Graphs (Bar Graphs, Line Plots, Pictographs)  7.4. Mean, Median, and Mode  7.5. Range of Data  7.6. Introduction to Probability  7.7. Simple Events and Outcomes  7.8. Probability of Independent Events
  8. Ratios and Proportions  8.1. Understanding Ratios  8.2. Writing and Simplifying Ratios  8.3. Equivalent Ratios  8.4. Introduction to Proportions  8.5. Solving Proportion Problems
  9. Algebraic Thinking  9.1. Understanding Variables and Expressions  9.2. Writing Algebraic Expressions  9.3. Simplifying Expressions  9.4. Solving One-Step Equations  9.5. Understanding Patterns and Sequences  9.6. Using the Distributive Property
  10. Financial Literacy  10.1. Introduction to Money and Currency  10.2. Budgeting Basics  10.3. Saving and Spending  10.4. Understanding Interest  10.5. Basic Financial Planning  10.6. Simple vs. Compound Interest

Grade 5 → Geometry ↓


Classifying Triangles


Triangles are one of the most fundamental shapes in geometry. They have three sides, three angles, and three vertices. Triangles come in many different shapes and sizes, but we can classify them into different types based on their sides and angles. This classification helps us understand their properties and use them in various geometric problems.

Types of triangles according to sides

Let us first look at how we classify triangles based on their sides. There are three main types:

Equilateral triangle

The three sides of an equilateral triangle are the same length. This also means that the three angles are the same: 60 degrees each. You can think of an equilateral triangle as perfectly balanced. No matter how you turn it, it looks the same.

    A /  /  B-----C AB = BC = CA
    A /  /  B-----C AB = BC = CA

In the above triangle AB, BC and CA are all equal. So it is an equilateral triangle.

Isosceles triangle

An isosceles triangle has two sides of equal length, and as a result, the two angles opposite these sides are also equal. This triangle looks symmetrical along the axis where the equal sides meet.

    A /  /  B-----C AB = AC
    A /  /  B-----C AB = AC

In this case, AB equals AC. Thus, the angles at B and C are equal.

Scalene triangle

The scalene triangle has all of its sides different lengths, and as a result, all three angles are different too. This means it has no symmetry like either of the other two types.

    A /  /  B-----C AB ≠ BC ≠ CA
    A /  /  B-----C AB ≠ BC ≠ CA

Here, no sides are equal. Therefore, each angle is unique.

Types of triangles based on angles

Now, let's talk about classifying triangles based on their angles. There are three main types:

Acute triangle

All three angles of an acute-angled triangle are less than 90 degrees. All angles are acute, so it is called an acute-angled triangle.

    A /  /  B-----C ∠A < 90°, ∠B < 90°, ∠C < 90°
    A /  /  B-----C ∠A < 90°, ∠B < 90°, ∠C < 90°

Each angle in this triangle is less than 90 degrees, making it an acute triangle.

Right triangle

A right triangle has one angle that is exactly 90 degrees. This triangle looks like it has a perfect "corner," making it easy to identify.

    A /| / | B--C ∠B = 90°
    A /| / | B--C ∠B = 90°

Angle ∠B is a right angle, so it is a right-angled triangle.

Obtuse-angled triangle

An obtuse triangle has one angle greater than 90 degrees. This makes the triangle appear more "stretched out" on one side.

    A /  /  B-----C ∠A > 90°
    A /  /  B-----C ∠A > 90°

If the angle ∠A is more than 90 degrees, then the triangle will be obtuse-angled.

Properties of triangles

Understanding triangles also means knowing some of their basic properties:

  • The sum of the angles in any triangle is 180 degrees. This is true for any type of triangle, whether it is based on sides or angles.

  • The length of any one side of a triangle must be less than the sum of the lengths of the other two sides. This is called the Triangle Inequality Theorem.

Examples for practice

Classifying triangles can be best learned through practice. Here are some examples to help you understand the concepts better.

Example 1

Take a triangle with sides 5 cm, 5 cm and 5 cm.

All sides of this triangle are equal. What type of triangle is this?

Since all sides are equal, it is an equilateral triangle.

Example 2

Consider a triangle with angles 60°, 60°, and 60°.

All angles are equal, and they are less than 90°. What kind of triangle is this?

This is an acute equilateral triangle. All angles are equal and less than 90°.

Example 3

Imagine a triangle with sides 4 cm, 4 cm and 6 cm and angles 80°, 80° and 20°.

Here two sides are equal and two angles are equal. What kind of triangle is this?

Since it has two equal sides and angles, it is an isosceles triangle.

Example 4

Take a triangle whose one angle is 90° and sides are 3 cm, 4 cm and 5 cm.

Its angle is a right angle. What kind of triangle is this?

This triangle is a right angled triangle.

Example 5

Consider a triangle with sides 7 cm, 8 cm and 9 cm.

None of its sides are equal. What kind of triangle is this?

Since all sides are different, it is a scalene triangle.

Conclusion

Understanding how to classify triangles helps us in geometry because it makes it easier to solve problems and understand shapes. By identifying triangles by the lengths of their sides or the measures of their angles, we can make informed guesses about their properties and learn how they might behave in geometric proofs or real-world applications. Triangles are everywhere, from bridges and buildings to art and nature, reinforcing their importance as foundational elements in both mathematics and life.


Grade 5 → 6.3


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Classifying Triangles

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