Types of Triangles (Grade 5)
A triangle is a closed figure with three sides, three angles, and three vertices. It is the simplest polygon — you cannot make a closed figure with fewer than three straight sides.
Triangles can be classified in two ways: by their sides and by their angles. Each classification tells us something different about the shape.
In Class 5, you will learn to identify and classify all types of triangles, understand their properties, apply the triangle inequality rule, and solve problems involving classification and angle calculation.
What is Types of Triangles - Class 5 Maths (Geometry)?
A triangle is a polygon with exactly three sides and three angles. The sum of all interior angles of a triangle is always 180°.
Triangles are classified into two main groups:
- Based on sides: Equilateral, Isosceles, Scalene
- Based on angles: Acute, Right, Obtuse
Triangle Inequality Rule: For any three lengths to form a triangle, the sum of any two sides must be greater than the third side. If this rule fails, no triangle can be formed.
Key properties all triangles share:
- Sum of interior angles = 180°
- The longest side is opposite the largest angle.
- The shortest side is opposite the smallest angle.
- Sum of any two sides > third side (triangle inequality).
Types of Triangles (Grade 5) Formula
Sum of angles of any triangle = 180°
Types and Properties
Classification by Sides:
| Type | Sides | Angles |
|---|---|---|
| Equilateral | All 3 sides equal | All 3 angles = 60° |
| Isosceles | 2 sides equal | 2 base angles equal |
| Scalene | All 3 sides different | All 3 angles different |
Classification by Angles:
| Type | Condition | Example Angles |
|---|---|---|
| Acute Triangle | All angles less than 90° | 60°, 70°, 50° |
| Right Triangle | One angle = 90° | 90°, 45°, 45° |
| Obtuse Triangle | One angle > 90° | 120°, 30°, 30° |
Combined classification: A triangle can be described using both systems. For example, a triangle with sides 5 cm, 5 cm, 5 cm and all angles 60° is an equilateral acute triangle. A triangle with sides 3 cm, 4 cm, 5 cm and one angle 90° is a scalene right triangle.
Solved Examples
Example 1: Example 1: Classify by Sides
Problem: Classify a triangle with sides 7 cm, 7 cm, and 7 cm.
Solution:
Step 1: All three sides are equal (7 cm each).
Step 2: A triangle with all three sides equal is called equilateral.
Answer: Equilateral triangle.
Example 2: Example 2: Classify by Sides
Problem: A triangle has sides 5 cm, 5 cm, and 8 cm. What type is it?
Solution:
Step 1: Two sides are equal (5 cm and 5 cm). The third side is different (8 cm).
Step 2: A triangle with exactly two equal sides is isosceles.
Answer: Isosceles triangle.
Example 3: Example 3: Classify by Sides
Problem: A triangle has sides 4 cm, 6 cm, and 9 cm. Classify it.
Solution:
Step 1: All three sides are different (4, 6, 9).
Step 2: A triangle with no equal sides is scalene.
Answer: Scalene triangle.
Example 4: Example 4: Classify by Angles
Problem: Classify a triangle with angles 60°, 70°, and 50°.
Solution:
Step 1: Check each angle: 60° < 90°, 70° < 90°, 50° < 90°.
Step 2: All three angles are less than 90°.
Answer: Acute triangle.
Example 5: Example 5: Classify by Angles
Problem: A triangle has angles 90°, 40°, and 50°. Classify it.
Solution:
Step 1: One angle is exactly 90°.
Step 2: A triangle with one 90° angle is a right triangle.
Answer: Right triangle.
Example 6: Example 6: Classify by Angles
Problem: A triangle has angles 25°, 35°, and 120°. Classify it.
Solution:
Step 1: One angle (120°) is greater than 90°.
Step 2: A triangle with one angle greater than 90° is obtuse.
Answer: Obtuse triangle.
Example 7: Example 7: Combined Classification
Problem: Rahul draws a triangle with sides 3 cm, 4 cm, 5 cm and one angle is 90°. Classify it by both sides and angles.
Solution:
Step 1: All three sides are different → Scalene.
Step 2: One angle is 90° → Right.
Answer: Scalene right triangle.
Example 8: Example 8: Can Such a Triangle Exist?
Problem: Can a triangle have sides 2 cm, 3 cm, and 6 cm?
Solution:
Step 1: For a triangle to exist, the sum of any two sides must be greater than the third side.
Step 2: Check: 2 + 3 = 5. But the third side is 6.
Step 3: 5 < 6, so the condition fails.
Answer: No, these sides cannot form a triangle.
Example 9: Example 9: Properties of Equilateral Triangle
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 is 8 cm.
Example 10: Example 10: Isosceles Triangle Angles
Problem: An isosceles triangle has one angle of 80° (between the two equal sides). Find the other two angles.
Solution:
Step 1: The two base angles are equal. Let each = x°.
Step 2: 80° + x + x = 180°
Step 3: 2x = 100°
Step 4: x = 50°
Answer: The other two angles are 50° each.
Real-World Applications
Where do we see different types of triangles?
- Equilateral triangles: Traffic yield signs, truss bridges, tent frames, and design patterns. They are the strongest triangle shape because the load is evenly distributed.
- Right triangles: Ramps, staircases, construction supports, and ladder-against-wall problems. The 3-4-5 right triangle is commonly used by carpenters to check corners are square.
- Isosceles triangles: Rooftops of houses, pizza slices, and kite designs. The two equal sides create a balanced, pleasing shape.
- Scalene triangles: Mountain slopes, irregular land plots, and many natural formations. They are the most common type found in real life.
Triangles in structures: The triangle is the strongest shape in engineering. Unlike rectangles (which can be pushed into parallelograms), a triangle holds its shape under pressure. That is why bridges, towers, and roofs use triangular structures.
Key Points to Remember
- Triangles are classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).
- An equilateral triangle has all sides and all angles (60°) equal.
- An isosceles triangle has two equal sides and two equal base angles.
- A scalene triangle has all sides and all angles different.
- An acute triangle has all angles less than 90°.
- A right triangle has exactly one 90° angle.
- An obtuse triangle has exactly one angle greater than 90°.
- The Triangle Inequality: the sum of any two sides must be greater than the third side.
Practice Problems
- Classify a triangle with sides 6 cm, 8 cm, and 10 cm by sides and by angles (given one angle is 90°).
- A triangle has angles 60°, 60°, and 60°. Classify it by angles and by sides.
- Can sides 1 cm, 2 cm, and 4 cm form a triangle? Explain.
- An isosceles triangle has equal sides of 10 cm each and a base of 12 cm. What is the perimeter?
- A triangle has angles 30°, 60°, and 90°. Classify it by angles. Is it scalene, isosceles, or equilateral?
- Meera says all equilateral triangles are also acute. Is she correct?
- A scalene triangle has one angle of 95°. Classify it by angles.
- Draw an isosceles right triangle. What are its three angles?
Frequently Asked Questions
Q1. How many types of triangles are there?
Triangles are classified into 3 types by sides (equilateral, isosceles, scalene) and 3 types by angles (acute, right, obtuse). So there are 6 basic types in total.
Q2. What is the difference between equilateral and isosceles triangles?
An equilateral triangle has all three sides equal and all angles 60°. An isosceles triangle has only two sides equal and two angles equal. Every equilateral triangle is also isosceles, but not every isosceles triangle is equilateral.
Q3. Can a triangle have two right angles?
No. Two right angles (90° + 90° = 180°) would leave 0° for the third angle, which is not possible.
Q4. What is the triangle inequality rule?
The sum of any two sides of a triangle must be greater than the third side. If this condition fails for any pair, the three lengths cannot form a triangle.
Q5. Can an equilateral triangle be a right triangle?
No. An equilateral triangle has all angles of 60°, so it cannot have a 90° angle.
Q6. Is an isosceles triangle always acute?
No. An isosceles triangle can be acute, right, or obtuse depending on the size of its angles. For example, an isosceles triangle with angles 120°, 30°, 30° is obtuse.
Q7. What type of triangle has all angles less than 90 degrees?
An acute triangle. All three of its angles are less than 90°.
Q8. Can a scalene triangle be a right triangle?
Yes. A triangle with sides 3 cm, 4 cm, 5 cm has all different sides (scalene) and one angle of 90° (right). This is a scalene right triangle.
Q9. What is the most common type of triangle in real life?
Scalene triangles are the most common in nature and everyday life because most triangles found in real objects have unequal sides. Right triangles are the most commonly used in construction and engineering.
Q10. Is this topic in the NCERT Class 5 syllabus?
Yes. Classification of triangles by sides and angles is part of the Geometry chapter in NCERT/CBSE Class 5 Maths.
Related Topics
- Angle Sum Property of Triangle
- Quadrilaterals (Grade 5)
- Lines, Line Segments and Rays
- Parallel and Perpendicular Lines
- Angles (Grade 5)
- Circles (Grade 5)
- Symmetry (Grade 5)
- Reflection and Rotation
- Nets of 3D Shapes (Grade 5)
- Views of 3D Shapes (Grade 5)
- Complementary and Supplementary Angles
- Constructing Triangles
