Classifying Triangles by Sides
Triangles can be classified based on the lengths of their sides. In Class 4, you learn three types: equilateral, isosceles, and scalene triangles. Each type has distinct properties that help in identification and construction.
Understanding triangle classification is important for geometry, art, architecture, and design. Triangles are the strongest shapes in engineering and appear everywhere in daily life.
What is Classifying Triangles by Sides - Class 4 Maths (Geometry)?
A triangle is a closed shape with 3 sides and 3 angles. Based on side lengths:
| Type | Sides | Angles |
|---|---|---|
| Equilateral | All 3 sides equal | All 3 angles = 60° |
| Isosceles | 2 sides equal | 2 angles equal |
| Scalene | No sides equal | No angles equal |
Solved Examples
Example 1: Example 1: Identifying an Equilateral Triangle
Problem: A triangle has sides 5 cm, 5 cm, and 5 cm. Classify it.
Solution:
All three sides are equal (5 cm = 5 cm = 5 cm).
Answer: It is an equilateral triangle.
Example 2: Example 2: Identifying an Isosceles Triangle
Problem: A triangle has sides 7 cm, 7 cm, and 4 cm. Classify it.
Solution:
Two sides are equal (7 cm = 7 cm), and the third is different (4 cm).
Answer: It is an isosceles triangle.
Example 3: Example 3: Identifying a Scalene Triangle
Problem: A triangle has sides 3 cm, 5 cm, and 6 cm. Classify it.
Solution:
All three sides are different (3 ≠ 5 ≠ 6).
Answer: It is a scalene triangle.
Example 4: Example 4: Finding the Missing Side
Problem: An equilateral triangle has a perimeter of 24 cm. Find the length of each side.
Solution:
Step 1: In an equilateral triangle, all sides are equal.
Step 2: Each side = Perimeter ÷ 3 = 24 ÷ 3 = 8 cm
Answer: Each side = 8 cm.
Example 5: Example 5: Isosceles Triangle Perimeter
Problem: An isosceles triangle has two equal sides of 9 cm each and a base of 6 cm. Find its perimeter.
Solution:
Perimeter = 9 + 9 + 6 = 24 cm
Answer: Perimeter = 24 cm.
Example 6: Example 6: Scalene Triangle Perimeter
Problem: A scalene triangle has sides 8 cm, 11 cm, and 14 cm. Find its perimeter.
Solution:
Perimeter = 8 + 11 + 14 = 33 cm
Answer: Perimeter = 33 cm.
Example 7: Example 7: Word Problem
Problem: Arjun has a triangular garden with sides 12 m, 12 m, and 15 m. What type of triangle is it? How much fencing does he need?
Solution:
Two sides equal → Isosceles triangle.
Fencing = Perimeter = 12 + 12 + 15 = 39 m
Answer: Isosceles triangle; fencing needed = 39 m.
Example 8: Example 8: Can These Form a Triangle?
Problem: Can sides 2 cm, 3 cm, and 8 cm form a triangle?
Solution:
Triangle inequality: The sum of any two sides must be greater than the third side.
2 + 3 = 5, which is less than 8.
Answer: No, these cannot form a triangle.
Example 9: Example 9: Classifying by Measurement
Problem: Measure the sides of a triangle: 4.5 cm, 6.2 cm, 4.5 cm. Classify it.
Solution:
Two sides are equal (4.5 cm = 4.5 cm), one is different (6.2 cm).
Answer: It is an isosceles triangle.
Example 10: Example 10: True or False
Problem: True or False: An equilateral triangle is also an isosceles triangle.
Solution:
An isosceles triangle has at least 2 equal sides. An equilateral triangle has 3 equal sides, which includes having 2 equal sides.
Answer: True. Every equilateral triangle is also isosceles, but not every isosceles triangle is equilateral.
Key Points to Remember
- Equilateral: All 3 sides equal, all angles 60°.
- Isosceles: 2 sides equal, 2 angles equal.
- Scalene: No sides equal, no angles equal.
- Every equilateral triangle is also isosceles (but not the reverse).
- Triangle inequality: The sum of any two sides must be greater than the third side.
- Perimeter of a triangle = sum of all three sides.
Practice Problems
- Classify a triangle with sides 10 cm, 10 cm, and 10 cm.
- Classify a triangle with sides 6 cm, 8 cm, and 10 cm.
- An equilateral triangle has a perimeter of 18 cm. Find each side.
- An isosceles triangle has equal sides of 7 cm and perimeter 20 cm. Find the third side.
- Can sides 4 cm, 4 cm, and 9 cm form a triangle?
- Neha drew a triangle with all sides of different lengths. What type is it?
- A triangular park has sides 50 m, 50 m, and 30 m. Classify it and find its perimeter.
Frequently Asked Questions
Q1. What is an equilateral triangle?
An equilateral triangle has all three sides of equal length. Each angle measures exactly 60°.
Q2. What is an isosceles triangle?
An isosceles triangle has two sides of equal length. The angles opposite to the equal sides are also equal.
Q3. What is a scalene triangle?
A scalene triangle has all three sides of different lengths. All three angles are also different.
Q4. Is an equilateral triangle also isosceles?
Yes. Since an equilateral triangle has all three sides equal, it automatically has at least two equal sides, satisfying the isosceles condition.
Q5. Can any three lengths form a triangle?
No. The sum of any two sides must be greater than the third side. This is called the triangle inequality. For example, 1 cm, 2 cm, and 5 cm cannot form a triangle because 1 + 2 = 3 < 5.
Q6. How do you find the perimeter of a triangle?
Add all three side lengths. For an equilateral triangle, perimeter = 3 x side length. For an isosceles triangle, perimeter = 2 x equal side + base.
Q7. What is the sum of angles in a triangle?
The sum of all three angles in any triangle is always 180°.
Q8. Is classifying triangles by sides part of NCERT Class 4?
Yes, identifying and classifying triangles by their sides is part of the CBSE/NCERT Class 4 Maths curriculum under the Geometry chapter.
