Introduction

In Year 7 Maths, students learn to classify triangles based on their sides and angles. Triangles are one of the basic shapes in geometry, and understanding the different types of triangles helps students solve problems involving angles, areas, and perimeters. Triangles can be classified by their side lengths and angles, and this classification helps distinguish between the various types of triangles.

Types of Triangles

1. Classification by Sides:

• Equilateral Triangle: All three sides are equal, and all three angles are equal ($$60^\circ$$ each).
• Isosceles Triangle: Two sides are equal, and the angles opposite these sides are equal.
• Scalene Triangle: All three sides and angles are different.

2. Classification by Angles:

• Acute Triangle: All three angles are less than $$90^\circ$$.
• Right-Angled Triangle: One of the angles is exactly $$90^\circ$$.
• Obtuse Triangle: One of the angles is greater than $$90^\circ$$.

Understanding these classifications is key to solving a variety of triangle-related problems in mathematics.

Classifying Triangles: Questions

Level 1: Easy

Identify the type of triangle by its sides:

1. A triangle with sides of 5 cm, 5 cm, and 5 cm.
2. A triangle with sides of 6 cm, 6 cm, and 8 cm.
3. A triangle with sides of 4 cm, 5 cm, and 6 cm.
4. A triangle with sides of 7 cm, 7 cm, and 7 cm.
5. A triangle with sides of 3 cm, 4 cm, and 5 cm.
6. A triangle with sides of 8 cm, 6 cm, and 8 cm.
7. A triangle with sides of 10 cm, 12 cm, and 15 cm.
8. A triangle with sides of 9 cm, 9 cm, and 9 cm.
9. A triangle with sides of 2 cm, 3 cm, and 4 cm.
10. A triangle with sides of 7 cm, 10 cm, and 12 cm.

Identify the type of triangle by its angles:

11. A triangle with angles of $$60^\circ$$, $$60^\circ$$, and $$60^\circ$$.
12. A triangle with angles of $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$.
13. A triangle with angles of $$100^\circ$$, $$40^\circ$$, and $$40^\circ$$.
14. A triangle with angles of $$50^\circ$$, $$50^\circ$$, and $$80^\circ$$.
15. A triangle with angles of $$70^\circ$$, $$50^\circ$$, and $$60^\circ$$.
16. A triangle with angles of $$90^\circ$$, $$30^\circ$$, and $$60^\circ$$.
17. A triangle with angles of $$120^\circ$$, $$30^\circ$$, and $$30^\circ$$.
18. A triangle with angles of $$85^\circ$$, $$45^\circ$$, and $$50^\circ$$.
19. A triangle with angles of $$75^\circ$$, $$60^\circ$$, and $$45^\circ$$.
20. A triangle with angles of $$110^\circ$$, $$35^\circ$$, and $$35^\circ$$.

Level 2: Medium

Classify the following triangles by their sides and angles:

1. A triangle with sides of 5 cm, 5 cm, and 5 cm and angles of $$60^\circ$$ each.
2. A triangle with sides of 7 cm, 5 cm, and 5 cm and angles of $$40^\circ$$, $$70^\circ$$, and $$70^\circ$$.
3. A triangle with sides of 4 cm, 4 cm, and 6 cm and angles of $$50^\circ$$, $$50^\circ$$, and $$80^\circ$$.
4. A triangle with sides of 9 cm, 7 cm, and 5 cm and angles of $$40^\circ$$, $$50^\circ$$, and $$90^\circ$$.
5. A triangle with sides of 3 cm, 3 cm, and 4 cm and angles of $$60^\circ$$, $$60^\circ$$, and $$60^\circ$$.
6. A triangle with sides of 6 cm, 8 cm, and 10 cm and angles of $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$.
7. A triangle with sides of 6 cm, 6 cm, and 8 cm and angles of $$60^\circ$$, $$60^\circ$$, and $$60^\circ$$.
8. A triangle with sides of 9 cm, 7 cm, and 7 cm and angles of $$60^\circ$$, $$70^\circ$$, and $$50^\circ$$.
9. A triangle with sides of 10 cm, 12 cm, and 15 cm and angles of $$90^\circ$$, $$30^\circ$$, and $$60^\circ$$.
10. A triangle with sides of 5 cm, 5 cm, and 8 cm and angles of $$50^\circ$$, $$65^\circ$$, and $$65^\circ$$.

Level 3: Hard

For each triangle, classify by its sides and angles:

1. Sides: 12 cm, 12 cm, 12 cm; angles: $$60^\circ$$ each.
2. Sides: 6 cm, 8 cm, 10 cm; angles: $$90^\circ$$, $$30^\circ$$, and $$60^\circ$$.
3. Sides: 9 cm, 12 cm, 15 cm; angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$.
4. Sides: 5 cm, 6 cm, 7 cm; angles: $$70^\circ$$, $$50^\circ$$, and $$60^\circ$$.
5. Sides: 10 cm, 10 cm, 14 cm; angles: $$100^\circ$$, $$40^\circ$$, and $$40^\circ$$.
6. Sides: 7 cm, 7 cm, 9 cm; angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$.
7. Sides: 11 cm, 11 cm, 15 cm; angles: $$110^\circ$$, $$35^\circ$$, and $$35^\circ$$.
8. Sides: 8 cm, 10 cm, 12 cm; angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$.
9. Sides: 6 cm, 6 cm, 8 cm; angles: $$80^\circ$$, $$60^\circ$$, and $$40^\circ$$.
10. Sides: 5 cm, 8 cm, 10 cm; angles: $$90^\circ$$, $$30^\circ$$, and $$60^\circ$$.

Identify whether these triangles are scalene, isosceles, or equilateral and if they are acute, right-angled, or obtuse:

11. Sides: 15 cm, 12 cm, 9 cm; angles: $$90^\circ$$, $$60^\circ$$, and $$30^\circ$$.
12. Sides: 9 cm, 9 cm, 9 cm; angles: $$60^\circ$$ each.
13. Sides: 6 cm, 6 cm, 8 cm; angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$.
14. Sides: 7 cm, 7 cm, 7 cm; angles: $$60^\circ$$ each.
15. Sides: 8 cm, 10 cm, 12 cm; angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$.
16. Sides: 5 cm, 5 cm, 8 cm; angles: $$50^\circ$$, $$65^\circ$$, and $$65^\circ$$.
17. Sides: 7 cm, 10 cm, 12 cm; angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$.
18. Sides: 6 cm, 6 cm, 6 cm; angles: $$60^\circ$$ each.
19. Sides: 10 cm, 14 cm, 12 cm; angles: $$90^\circ$$, $$30^\circ$$, and $$60^\circ$$.
20. Sides: 8 cm, 8 cm, 8 cm; angles: $$60^\circ$$ each.

Answers with Explanations: Classifying Triangles

Level 1: Easy

Identify the type of triangle by its sides:

1. A triangle with sides of 5 cm, 5 cm, and 5 cm:
   Equilateral — All three sides are equal, so the triangle is equilateral.
2. A triangle with sides of 6 cm, 6 cm, and 8 cm:
   Isosceles — Two sides are equal, making it an isosceles triangle.
3. A triangle with sides of 4 cm, 5 cm, and 6 cm:
   Scalene — All sides are different, so the triangle is scalene.
4. A triangle with sides of 7 cm, 7 cm, and 7 cm:
   Equilateral — All three sides are equal, so the triangle is equilateral.
5. A triangle with sides of 3 cm, 4 cm, and 5 cm:
   Scalene — All sides are different, so the triangle is scalene.
6. A triangle with sides of 8 cm, 6 cm, and 8 cm:
   Isosceles — Two sides are equal, making it an isosceles triangle.
7. A triangle with sides of 10 cm, 12 cm, and 15 cm:
   Scalene — All sides are different, so the triangle is scalene.
8. A triangle with sides of 9 cm, 9 cm, and 9 cm:
   Equilateral — All three sides are equal, so the triangle is equilateral.
9. A triangle with sides of 2 cm, 3 cm, and 4 cm:
   Scalene — All sides are different, so the triangle is scalene.
10. A triangle with sides of 7 cm, 10 cm, and 12 cm:
    Scalene — All sides are different, so the triangle is scalene.

Identify the type of triangle by its angles:

11. A triangle with angles of $$60^\circ$$, $$60^\circ$$, and $$60^\circ$$:
    Equilateral — All angles are equal, and all are $$60^\circ$$, so the triangle is equilateral.
12. A triangle with angles of $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$:
    Right-angled Isosceles — One angle is $$90^\circ$$, making it a right-angled triangle, and two angles are equal, so it’s also isosceles.
13. A triangle with angles of $$100^\circ$$, $$40^\circ$$, and $$40^\circ$$:
    Obtuse Isosceles — One angle is greater than $$90^\circ$$, so it’s obtuse, and two angles are equal, making it isosceles.
14. A triangle with angles of $$50^\circ$$, $$50^\circ$$, and $$80^\circ$$:
    Isosceles — Two angles are equal, making it an isosceles triangle.
15. A triangle with angles of $$70^\circ$$, $$50^\circ$$, and $$60^\circ$$:
    Scalene Acute — All angles are different, and each is less than $$90^\circ$$, making it an acute scalene triangle.
16. A triangle with angles of $$90^\circ$$, $$30^\circ$$, and $$60^\circ$$:
    Right-Angled Scalene — One angle is $$90^\circ$$, making it a right-angled triangle, and all angles are different.
17. A triangle with angles of $$120^\circ$$, $$30^\circ$$, and $$30^\circ$$:
    Obtuse Isosceles — One angle is greater than $$90^\circ$$, and two angles are equal, making it obtuse and isosceles.
18. A triangle with angles of $$85^\circ$$, $$45^\circ$$, and $$50^\circ$$:
    Acute Scalene — All angles are less than $$90^\circ$$ and different.
19. A triangle with angles of $$75^\circ$$, $$60^\circ$$, and $$45^\circ$$:
    Acute Scalene — All angles are less than $$90^\circ$$ and different.
20. A triangle with angles of $$110^\circ$$, $$35^\circ$$, and $$35^\circ$$:
    Obtuse Isosceles — One angle is greater than $$90^\circ$$, and two angles are equal, making it obtuse and isosceles.

Level 2: Medium

Classify the following triangles by their sides and angles:

1. Sides: 5 cm, 5 cm, and 5 cm; Angles: $$60^\circ$$ each:
   Equilateral, Acute — All sides and angles are equal, and each angle is less than $$90^\circ$$.
2. Sides: 7 cm, 5 cm, and 5 cm; Angles: $$40^\circ$$, $$70^\circ$$, and $$70^\circ$$:
   Isosceles, Acute — Two sides and two angles are equal, and all angles are less than $$90^\circ$$.
3. Sides: 4 cm, 4 cm, and 6 cm; Angles: $$50^\circ$$, $$50^\circ$$, and $$80^\circ$$:
   Isosceles, Acute — Two sides and two angles are equal, and all angles are less than $$90^\circ$$.
4. Sides: 9 cm, 7 cm, and 5 cm; Angles: $$40^\circ$$, $$50^\circ$$, and $$90^\circ$$:
   Scalene, Right-Angled — All sides and angles are different, and one angle is $$90^\circ$$.
5. Sides: 3 cm, 3 cm, and 4 cm; Angles: $$60^\circ$$, $$60^\circ$$, and $$60^\circ$$:
   Equilateral, Acute — All sides and angles are equal, and each angle is less than $$90^\circ$$.
6. Sides: 6 cm, 8 cm, and 10 cm; Angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$:
   Scalene, Right-Angled — All sides and angles are different, and one angle is $$90^\circ$$.
7. Sides: 6 cm, 6 cm, and 8 cm; Angles: $$60^\circ$$, $$60^\circ$$, and $$60^\circ$$:
   Isosceles, Acute — Two sides are equal, and all angles are less than $$90^\circ$$.
8. Sides: 9 cm, 7 cm, and 7 cm; Angles: $$60^\circ$$, $$70^\circ$$, and $$50^\circ$$:
   Isosceles, Acute — Two sides and two angles are equal, and all angles are less than $$90^\circ$$.
9. Sides: 10 cm, 12 cm, and 15 cm; Angles: $$90^\circ$$, $$30^\circ$$, and $$60^\circ$$:
   Scalene, Right-Angled — All sides and angles are different, and one angle is $$90^\circ$$.
10. Sides: 5 cm, 5 cm, and 8 cm; Angles: $$50^\circ$$, $$65^\circ$$, and $$65^\circ$$:
    Isosceles, Acute — Two sides and two angles are equal, and all angles are less than $$90^\circ$$.

Level 3: Hard

For each triangle, classify by its sides and angles:

1. Sides: 12 cm, 12 cm, 12 cm; Angles: $$60^\circ$$ each:
   Equilateral, Acute — All sides and angles are equal, and each angle is less than $$90^\circ$$.
2. Sides: 6 cm, 8 cm, 10 cm; Angles: $$90^\circ$$, $$30^\circ$$, and $$60^\circ$$:
   Scalene, Right-Angled — All sides are different, and one angle is $$90^\circ$$.
3. Sides: 9 cm, 12 cm, 15 cm; Angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$:
   Scalene, Right-Angled — All sides are different, and one angle is $$90^\circ$$.
4. Sides: 5 cm, 6 cm, 7 cm; Angles: $$70^\circ$$, $$50^\circ$$, and $$60^\circ$$:
   Scalene, Acute — All sides and angles are different, and all angles are less than $$90^\circ$$.
5. Sides: 10 cm, 10 cm, 14 cm; Angles: $$100^\circ$$, $$40^\circ$$, and $$40^\circ$$:
   Isosceles, Obtuse — Two sides are equal, and one angle is greater than $$90^\circ$$.
6. Sides: 7 cm, 7 cm, 9 cm; Angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$:
   Isosceles, Right-Angled — Two sides are equal, and one angle is $$90^\circ$$.
7. Sides: 11 cm, 11 cm, 15 cm; Angles: $$110^\circ$$, $$35^\circ$$, and $$35^\circ$$:
   Isosceles, Obtuse — Two sides are equal, and one angle is greater than $$90^\circ$$.
8. Sides: 8 cm, 10 cm, 12 cm; Angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$:
   Scalene, Right-Angled — All sides are different, and one angle is $$90^\circ$$.
9. Sides: 6 cm, 6 cm, 8 cm; Angles: $$80^\circ$$, $$60^\circ$$, and $$40^\circ$$:
   Isosceles, Acute — Two sides are equal, and all angles are less than $$90^\circ$$.
10. Sides: 5 cm, 8 cm, 10 cm; Angles: $$90^\circ$$, $$30^\circ$$, and $$60^\circ$$:
    Scalene, Right-Angled — All sides and angles are different, and one angle is $$90^\circ$$.

Identify whether these triangles are scalene, isosceles, or equilateral and if they are acute, right-angled, or obtuse:

11. Sides: 15 cm, 12 cm, 9 cm; Angles: $$90^\circ$$, $$60^\circ$$, and $$30^\circ$$:
    Scalene, Right-Angled — All sides are different, and one angle is $$90^\circ$$.
12. Sides: 9 cm, 9 cm, 9 cm; Angles: $$60^\circ$$ each:
    Equilateral, Acute — All sides and angles are equal, and all angles are less than $$90^\circ$$.
13. Sides: 6 cm, 6 cm, 8 cm; Angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$:
    Isosceles, Right-Angled — Two sides are equal, and one angle is $$90^\circ$$.
14. Sides: 7 cm, 7 cm, 7 cm; Angles: $$60^\circ$$ each:
    Equilateral, Acute — All sides and angles are equal, and all angles are less than $$90^\circ$$.
15. Sides: 8 cm, 10 cm, 12 cm; Angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$:
    Scalene, Right-Angled — All sides are different, and one angle is $$90^\circ$$.
16. Sides: 5 cm, 5 cm, 8 cm; Angles: $$50^\circ$$, $$65^\circ$$, and $$65^\circ$$:
    Isosceles, Acute — Two sides are equal, and all angles are less than $$90^\circ$$.
17. Sides: 7 cm, 10 cm, 12 cm; Angles: $$90^\circ$$, $$45^\circ$$, and $$45^\circ$$:
    Scalene, Right-Angled — All sides are different, and one angle is $$90^\circ$$.
18. Sides: 6 cm, 6 cm, 6 cm; Angles: $$60^\circ$$ each:
    Equilateral, Acute — All sides and angles are equal, and all angles are less than $$90^\circ$$.
19. Sides: 10 cm, 14 cm, 12 cm; Angles: $$90^\circ$$, $$30^\circ$$, and $$60^\circ$$:
    Scalene, Right-Angled — All sides and angles are different, and one angle is $$90^\circ$$.
20. Sides: 8 cm, 8 cm, 8 cm; Angles: $$60^\circ$$ each:
    Equilateral, Acute — All sides and angles are equal, and all angles are less than $$90^\circ$$.

These answers provide students with a full explanation of how to classify triangles based on their sides and angles. Each step reinforces the key properties of equilateral, isosceles, and scalene triangles, as well as acute, right-angled, and obtuse angles.