Triangle Worksheets - Math Monks - Free Printable

Problem Overview:

The task involves classifying triangles into two categories:
1. By Angles: Acute, Obtuse, or Right.
2. By Sides: Equilateral, Isosceles, or Scalene.

We will solve this step by step for each triangle.

---

Part 1: Classify Triangles by Angles

#### Rules for Classification by Angles:
- Acute Triangle: All angles are less than 90°.
- Right Triangle: One angle is exactly 90°.
- Obtuse Triangle: One angle is greater than 90°.

#### Triangles 1 to 6:

1. Triangle 1:
- Angles: 45°, 45°, 90°
- One angle is 90°.
- Classification: Right Triangle.

2. Triangle 2:
- Angles: 60°, 60°, 60°
- All angles are less than 90°.
- Classification: Acute Triangle.

3. Triangle 3:
- Angles: 140°, 40°, 10°
- One angle is 140° (greater than 90°).
- Classification: Obtuse Triangle.

4. Triangle 4:
- Angles: 50°, 92°, 38°
- One angle is 92° (greater than 90°).
- Classification: Obtuse Triangle.

5. Triangle 5:
- Angles: 40°, 60°, 80°
- All angles are less than 90°.
- Classification: Acute Triangle.

6. Triangle 6:
- Angles: 60°, 70°, 50°
- All angles are less than 90°.
- Classification: Acute Triangle.

---

Part 2: Classify Triangles by Sides

#### Rules for Classification by Sides:
- Equilateral Triangle: All three sides are equal.
- Isosceles Triangle: At least two sides are equal.
- Scalene Triangle: All three sides are different.

#### Triangles 7 to 12:

7. Triangle 7:
- Sides: 4 cm, 5 cm, 6 cm
- All sides are different.
- Classification: Scalene Triangle.

8. Triangle 8:
- Sides: 4.5 in, 6.5 in, 7.5 in
- All sides are different.
- Classification: Scalene Triangle.

9. Triangle 9:
- Sides: 9 yd, 9 yd, 12 yd
- Two sides are equal (9 yd, 9 yd).
- Classification: Isosceles Triangle.

10. Triangle 10:
- Sides: 4.5 cm, 4.5 cm, 4.5 cm
- All three sides are equal.
- Classification: Equilateral Triangle.

11. Triangle 11:
- Sides: 4 cm, 12 cm, 11 cm
- All sides are different.
- Classification: Scalene Triangle.

12. Triangle 12:
- Sides: 3.5 cm, 3.5 cm, 6 cm
- Two sides are equal (3.5 cm, 3.5 cm).
- Classification: Isosceles Triangle.

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Final Answer:

Combining the classifications for both parts:

| Triangle | By Angles | By Sides |
|----------|------------------|------------------|
| 1 | Right Triangle | Scalene Triangle |
| 2 | Acute Triangle | Equilateral Triangle |
| 3 | Obtuse Triangle | Scalene Triangle |
| 4 | Obtuse Triangle | Scalene Triangle |
| 5 | Acute Triangle | Scalene Triangle |
| 6 | Acute Triangle | Scalene Triangle |
| 7 | Not applicable | Scalene Triangle |
| 8 | Not applicable | Scalene Triangle |
| 9 | Not applicable | Isosceles Triangle |
| 10 | Not applicable | Equilateral Triangle |
| 11 | Not applicable | Scalene Triangle |
| 12 | Not applicable | Isosceles Triangle |

$$
\boxed{
\begin{array}{c|c|c}
\text{Triangle} & \text{By Angles} & \text{By Sides} \\
\hline
1 & \text{Right Triangle} & \text{Scalene Triangle} \\
2 & \text{Acute Triangle} & \text{Equilateral Triangle} \\
3 & \text{Obtuse Triangle} & \text{Scalene Triangle} \\
4 & \text{Obtuse Triangle} & \text{Scalene Triangle} \\
5 & \text{Acute Triangle} & \text{Scalene Triangle} \\
6 & \text{Acute Triangle} & \text{Scalene Triangle} \\
7 & \text{Not applicable} & \text{Scalene Triangle} \\
8 & \text{Not applicable} & \text{Scalene Triangle} \\
9 & \text{Not applicable} & \text{Isosceles Triangle} \\
10 & \text{Not applicable} & \text{Equilateral Triangle} \\
11 & \text{Not applicable} & \text{Scalene Triangle} \\
12 & \text{Not applicable} & \text{Isosceles Triangle} \\
\end{array}
}
$$