Classifying Triangles by Sides and Angles - A math worksheet for identifying equilateral, isosceles, scalene, acute, right, and obtuse triangles.

Problem Overview:

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

We will analyze each triangle in the image and classify them accordingly.

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Part 1: Classifying Triangles by Sides

#### Definitions:
- Equilateral Triangle: All three sides are equal.
- Isosceles Triangle: At least two sides are equal.
- Scalene Triangle: No sides are equal.

#### Analysis of Each Triangle:

1. Triangle 1:
- Sides: None of the sides appear to be equal.
- Classification: Scalene

2. Triangle 2:
- Sides: Two sides are marked as equal (indicated by the same symbol).
- Classification: Isosceles

3. Triangle 3:
- Sides: None of the sides appear to be equal.
- Classification: Scalene

4. Triangle 4:
- Sides: Two sides are marked as equal (indicated by the same symbol).
- Classification: Isosceles

5. Triangle 5:
- Sides: All three sides are marked as equal (indicated by the same symbol).
- Classification: Equilateral

6. Triangle 6:
- Sides: None of the sides appear to be equal.
- Classification: Scalene

---

Part 2: Classifying Triangles by Angles

#### Definitions:
- Acute Triangle: All angles are less than 90°.
- Right Triangle: One angle is exactly 90°.
- Obtuse Triangle: One angle is greater than 90°.

#### Analysis of Each Triangle:

7. Triangle 7:
- Angles: One angle appears to be greater than 90°.
- Classification: Obtuse

8. Triangle 8:
- Angles: All angles appear to be less than 90°.
- Classification: Acute

9. Triangle 9:
- Angles: One angle is exactly 90° (right angle).
- Classification: Right

10. Triangle 10:
- Angles: One angle appears to be greater than 90°.
- Classification: Obtuse

11. Triangle 11:
- Angles: One angle is exactly 90° (right angle).
- Classification: Right

12. Triangle 12:
- Angles: All angles appear to be less than 90°.
- Classification: Acute

---

Final Answer:

#### By Sides:
1. Scalene
2. Isosceles
3. Scalene
4. Isosceles
5. Equilateral
6. Scalene

#### By Angles:
7. Obtuse
8. Acute
9. Right
10. Obtuse
11. Right
12. Acute

$$
\boxed{
\text{By Sides: Scalene, Isosceles, Scalene, Isosceles, Equilateral, Scalene}
}
$$
$$
\boxed{
\text{By Angles: Obtuse, Acute, Right, Obtuse, Right, Acute}
}
$$