Types of Triangles (Grade 4)
A triangle is a closed shape with three sides and three angles. Triangles are the simplest polygons and appear everywhere — in rooftops, traffic signs, and sandwich slices.
In Class 4, you will learn to classify triangles based on the length of their sides and the size of their angles.
What is Types of Triangles - Class 4 Maths (Geometry)?
A triangle is a polygon with exactly 3 sides, 3 vertices (corners), and 3 angles. The sum of all three angles in any triangle is always 180°.
Types of Triangles (Grade 4) Formula
Sum of angles in a triangle = 180°
If two angles of a triangle are known, the third angle = 180° − (first angle + second angle).
Types and Properties
Classification by Sides:
| Type | Sides | Example |
|---|---|---|
| Equilateral Triangle | All 3 sides are equal | A triangle with sides 5 cm, 5 cm, 5 cm |
| Isosceles Triangle | Any 2 sides are equal | A triangle with sides 6 cm, 6 cm, 4 cm |
| Scalene Triangle | All 3 sides are different | A triangle with sides 3 cm, 5 cm, 7 cm |
Classification by Angles:
| Type | Angles |
|---|---|
| Acute-angled Triangle | All 3 angles are less than 90° |
| Right-angled Triangle | One angle is exactly 90° |
| Obtuse-angled Triangle | One angle is greater than 90° |
Every equilateral triangle is also acute-angled because each of its angles is 60°.
Solved Examples
Example 1: Example 1: Classify by sides
Problem: A triangle has sides 7 cm, 7 cm, and 7 cm. Classify it.
Solution:
Step 1: Compare all three sides: 7 = 7 = 7.
Step 2: All three sides are equal.
Answer: It is an equilateral triangle.
Example 2: Example 2: Isosceles triangle
Problem: Priya draws a triangle with sides 8 cm, 8 cm, and 5 cm. What type is it?
Solution:
Step 1: Two sides are equal (8 cm and 8 cm). The third side (5 cm) is different.
Answer: It is an isosceles triangle.
Example 3: Example 3: Scalene triangle
Problem: A triangle has sides 4 cm, 6 cm, and 9 cm. Classify it.
Solution:
Step 1: Compare: 4 ≠ 6 ≠ 9. All three sides are different.
Answer: It is a scalene triangle.
Example 4: Example 4: Classify by angles
Problem: A triangle has angles 50°, 60°, and 70°. Classify it by its angles.
Solution:
Step 1: Check each angle: 50° < 90°, 60° < 90°, 70° < 90°.
Step 2: All angles are acute (less than 90°).
Answer: It is an acute-angled triangle.
Example 5: Example 5: Right-angled triangle
Problem: Aman measures the angles of a triangle as 90°, 45°, and 45°. Classify it.
Solution:
Step 1: One angle is exactly 90°.
Step 2: Check sum: 90° + 45° + 45° = 180° ✓
Answer: It is a right-angled triangle. It is also isosceles (two equal angles of 45°).
Example 6: Example 6: Obtuse-angled triangle
Problem: A triangle has angles 30°, 40°, and 110°. Classify it by angles.
Solution:
Step 1: 110° > 90° — one angle is obtuse.
Step 2: Check sum: 30° + 40° + 110° = 180° ✓
Answer: It is an obtuse-angled triangle.
Example 7: Example 7: Finding the missing angle
Problem: Two angles of a triangle are 55° and 65°. Find the third angle and classify.
Solution:
Step 1: Third angle = 180° − 55° − 65° = 60°.
Step 2: All angles (55°, 60°, 65°) are less than 90°.
Answer: The third angle is 60°. The triangle is acute-angled and scalene (all angles are different, so all sides are different).
Example 8: Example 8: Equilateral triangle angles
Problem: Each side of a triangle is 6 cm. What is each angle?
Solution:
Step 1: All sides are equal → equilateral triangle.
Step 2: In an equilateral triangle, all three angles are equal.
Step 3: Each angle = 180° ÷ 3 = 60°.
Answer: Each angle is 60°.
Example 9: Example 9: Real-life triangle
Problem: Meera notices the triangular face of a roof. Two sides of the triangular face are 4 m each and the base is 6 m. What type of triangle is it?
Solution:
Step 1: Two sides are equal (4 m and 4 m). The base (6 m) is different.
Answer: The roof face is an isosceles triangle.
Example 10: Example 10: Can a triangle have two right angles?
Problem: Rahul asks — can a triangle have two angles of 90° each?
Solution:
Step 1: If two angles are 90° each, their sum = 90° + 90° = 180°.
Step 2: The total must be 180°, so the third angle = 180° − 180° = 0°.
Step 3: An angle of 0° is not possible in a triangle.
Answer: No, a triangle cannot have two right angles.
Real-World Applications
Triangles are used in many real-life structures:
- Roofs and bridges — triangular shapes provide strength and stability.
- Traffic signs — warning signs are often triangular (yield signs, caution signs).
- Musical instruments — the triangle instrument is shaped as a triangle.
- Sail boats — the sail is often a triangular shape.
- Pizza slices and sandwich halves — everyday triangle shapes.
Key Points to Remember
- A triangle has 3 sides, 3 angles, and 3 vertices.
- Sum of all angles = 180°.
- By sides: Equilateral (all equal), Isosceles (two equal), Scalene (all different).
- By angles: Acute (all < 90°), Right (one = 90°), Obtuse (one > 90°).
- An equilateral triangle has all angles = 60°.
- A triangle cannot have more than one right angle or more than one obtuse angle.
- A triangle can be classified both by sides and by angles (e.g., isosceles right-angled triangle).
Practice Problems
- Classify a triangle with sides 5 cm, 12 cm, and 13 cm by its sides.
- A triangle has angles 60°, 60°, and 60°. Classify by sides and angles.
- Two angles of a triangle are 35° and 55°. Find the third angle and classify the triangle by angles.
- Can a triangle have sides 3 cm, 3 cm, and 3 cm and still be scalene? Why or why not?
- Dev draws a triangle with one angle of 120°. What type is it by angles? Can the other two angles be obtuse?
- Neha measures the sides of a triangle as 9 cm, 9 cm, and 12 cm. Classify it.
- Draw any triangle. Measure all three angles with a protractor. Verify that they add up to 180°.
Frequently Asked Questions
Q1. What are the three types of triangles based on sides?
Equilateral (all 3 sides equal), isosceles (2 sides equal), and scalene (all 3 sides different).
Q2. What are the three types of triangles based on angles?
Acute-angled (all angles less than 90°), right-angled (one angle exactly 90°), and obtuse-angled (one angle more than 90°).
Q3. What is the sum of angles in a triangle?
The sum of all three interior angles in any triangle is always 180°.
Q4. Can a triangle be both equilateral and right-angled?
No. An equilateral triangle has all angles equal to 60°. None of its angles is 90°, so it cannot be right-angled.
Q5. Can a triangle have two obtuse angles?
No. Two obtuse angles would each be more than 90°, totalling more than 180°. Since the angle sum must be exactly 180°, at most one angle can be obtuse.
Q6. What does isosceles mean?
Isosceles means 'equal legs.' An isosceles triangle has exactly two sides of equal length. The angles opposite the equal sides are also equal.
Q7. Is every equilateral triangle also isosceles?
Yes. Since an equilateral triangle has all three sides equal, it automatically has at least two sides equal, meeting the definition of isosceles.
Q8. How do you find the third angle of a triangle?
Subtract the sum of the two known angles from 180°. For example, if two angles are 70° and 50°, the third angle = 180° − 70° − 50° = 60°.
Q9. Where do we see triangles in daily life?
Triangles appear in rooftops, bridges, traffic signs, pizza slices, sandwiches cut diagonally, hangers, and the frames of bicycles.
