Identifying Triangles Worksheet - Students identify and name triangles based on side lengths and angles.

To solve the problem of identifying and naming the triangles in the worksheet, we need to classify each triangle based on its sides and angles. Triangles can be classified into the following categories:

Classification Based on Sides:

1. Equilateral Triangle: All three sides are equal.
2. Isosceles Triangle: Two sides are equal.
3. Scalene Triangle: All three sides are different.

Classification Based on Angles:

1. Acute Triangle: All three angles are less than 90°.
2. Right Triangle: One angle is exactly 90°.
3. Obtuse Triangle: One angle is greater than 90°.

Now, let's analyze each triangle step by step:

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Triangle 1:

- Sides: 5 cm, 4 cm, 6 cm
- Angles: Not given.
- Classification:
- Sides: All sides are different → Scalene Triangle.
- Angles: Since no angle is 90° or > 90°, it is an Acute Triangle.
- Final Answer: Scalene Acute Triangle.

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Triangle 2:

- Sides: Not explicitly given, but all angles are 60°.
- Angles: 60°, 60°, 60°
- Classification:
- Sides: All angles are equal (60°), so all sides must be equal → Equilateral Triangle.
- Angles: All angles are less than 90° → Acute Triangle.
- Final Answer: Equilateral Acute Triangle.

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Triangle 3:

- Sides: 5 cm, 4.4 cm, 11 cm
- Angles: Not given.
- Classification:
- Sides: All sides are different → Scalene Triangle.
- Angles: The side lengths suggest one angle is obtuse (since 11² > 5² + 4.4²).
- Final Answer: Scalene Obtuse Triangle.

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Triangle 4:

- Sides: 3.5 cm, 3.5 cm, 3.5 cm
- Angles: Not given.
- Classification:
- Sides: All sides are equal → Equilateral Triangle.
- Angles: All angles are less than 90° → Acute Triangle.
- Final Answer: Equilateral Acute Triangle.

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Triangle 5:

- Sides: Not explicitly given, but angles are 80°, 50°, 50°.
- Angles: 80°, 50°, 50°
- Classification:
- Sides: Two angles are equal (50°), so two sides must be equal → Isosceles Triangle.
- Angles: All angles are less than 90° → Acute Triangle.
- Final Answer: Isosceles Acute Triangle.

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Triangle 6:

- Sides: Not explicitly given, but angles are 110°, 30°, 40°.
- Angles: 110°, 30°, 40°
- Classification:
- Sides: No information about sides, but one angle is 110° → Obtuse Triangle.
- Angles: One angle is greater than 90° → Obtuse Triangle.
- Final Answer: Scalene Obtuse Triangle.

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Triangle 7:

- Sides: Not explicitly given, but angles are 40°, 100°, 40°.
- Angles: 40°, 100°, 40°
- Classification:
- Sides: Two angles are equal (40°), so two sides must be equal → Isosceles Triangle.
- Angles: One angle is greater than 90° → Obtuse Triangle.
- Final Answer: Isosceles Obtuse Triangle.

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Triangle 8:

- Sides: Not explicitly given, but angles are 46°, 62°, 72°.
- Angles: 46°, 62°, 72°
- Classification:
- Sides: No information about sides, but all angles are less than 90° → Acute Triangle.
- Angles: All angles are less than 90° → Acute Triangle.
- Final Answer: Scalene Acute Triangle.

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Triangle 9:

- Sides: 4 cm, 3 cm, 5 cm
- Angles: Not given.
- Classification:
- Sides: All sides are different → Scalene Triangle.
- Angles: The side lengths suggest one angle is a right angle (since 5² = 4² + 3²).
- Final Answer: Scalene Right Triangle.

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Triangle 10:

- Sides: 4 cm, 15 cm, 13 cm
- Angles: Not given.
- Classification:
- Sides: All sides are different → Scalene Triangle.
- Angles: The side lengths suggest one angle is obtuse (since 15² > 4² + 13²).
- Final Answer: Scalene Obtuse Triangle.

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Triangle 11:

- Sides: 16 in, 16 in, 16 in
- Angles: Not given.
- Classification:
- Sides: All sides are equal → Equilateral Triangle.
- Angles: All angles are less than 90° → Acute Triangle.
- Final Answer: Equilateral Acute Triangle.

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Triangle 12:

- Sides: Not explicitly given, but angles are 110°, 35°, 35°.
- Angles: 110°, 35°, 35°
- Classification:
- Sides: Two angles are equal (35°), so two sides must be equal → Isosceles Triangle.
- Angles: One angle is greater than 90° → Obtuse Triangle.
- Final Answer: Isosceles Obtuse Triangle.

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Final Answers:

1. Scalene Acute Triangle
2. Equilateral Acute Triangle
3. Scalene Obtuse Triangle
4. Equilateral Acute Triangle
5. Isosceles Acute Triangle
6. Scalene Obtuse Triangle
7. Isosceles Obtuse Triangle
8. Scalene Acute Triangle
9. Scalene Right Triangle
10. Scalene Obtuse Triangle
11. Equilateral Acute Triangle
12. Isosceles Obtuse Triangle

$$
\boxed{
\begin{array}{ll}
1. & \text{Scalene Acute Triangle} \\
2. & \text{Equilateral Acute Triangle} \\
3. & \text{Scalene Obtuse Triangle} \\
4. & \text{Equilateral Acute Triangle} \\
5. & \text{Isosceles Acute Triangle} \\
6. & \text{Scalene Obtuse Triangle} \\
7. & \text{Isosceles Obtuse Triangle} \\
8. & \text{Scalene Acute Triangle} \\
9. & \text{Scalene Right Triangle} \\
10. & \text{Scalene Obtuse Triangle} \\
11. & \text{Equilateral Acute Triangle} \\
12. & \text{Isosceles Obtuse Triangle}
\end{array}
}
$$