Classify triangles by angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral) with diagrams and examples.

Problem: Classifying Triangles by Angles and Sides

The worksheet asks us to classify triangles based on their angles (acute, equiangular, right, or obtuse) and sides (scalene, isosceles, or equilateral). Let's solve each part step by step.

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#### Part 1: Classify each triangle by its angles

1. Triangle 1:
- All angles are less than 90°.
- Classification: Acute triangle.

2. Triangle 2:
- One angle is 150°, which is greater than 90°.
- Classification: Obtuse triangle.

3. Triangle 3:
- All angles are less than 90°.
- Classification: Acute triangle.

4. Triangle 4:
- One angle is 90°.
- Classification: Right triangle.

5. Triangle 5:
- All angles are less than 90°.
- Classification: Acute triangle.

6. Triangle 6:
- One angle is 90°.
- Classification: Right triangle.

7. Triangle 7:
- One angle is 140°, which is greater than 90°.
- Classification: Obtuse triangle.

8. Triangle 8:
- All angles are equal (each is 60°).
- Classification: Equiangular triangle.

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#### Part 2: Classify each triangle by its sides

9. Triangle 9:
- All sides are of different lengths.
- Classification: Scalene triangle.

10. Triangle 10:
- Two sides are marked as equal.
- Classification: Isosceles triangle.

11. Triangle 11:
- All sides are of different lengths.
- Classification: Scalene triangle.

12. Triangle 12:
- Two sides are marked as equal.
- Classification: Isosceles triangle.

13. Triangle 13:
- All sides are marked as equal.
- Classification: Equilateral triangle.

14. Triangle 14:
- All sides are of different lengths.
- Classification: Scalene triangle.

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#### Part 3: Complete the charts by classifying each triangle by its angles and by its sides

##### Problem 15:
- Triangle ΔABD:
- Angles: ∠A = 55°, ∠B = 70°, ∠ADB = 55° (since the sum of angles in a triangle is 180°).
- All angles are less than 90°.
- By Angles: Acute triangle.
- Sides: AB ≠ BD ≠ AD.
- By Sides: Scalene triangle.

- Triangle ΔDBC:
- Angles: ∠D = 55°, ∠B = 35°, ∠C = 90° (since the sum of angles in a triangle is 180°).
- One angle is 90°.
- By Angles: Right triangle.
- Sides: DB ≠ BC ≠ CD.
- By Sides: Scalene triangle.

- Triangle ΔABC:
- Angles: ∠A = 55°, ∠B = 70°, ∠C = 55° (since the sum of angles in a triangle is 180°).
- All angles are less than 90°.
- By Angles: Acute triangle.
- Sides: AB ≠ BC ≠ AC.
- By Sides: Scalene triangle.

##### Problem 16:
- Triangle ΔLMO:
- Angles: ∠L = 20°, ∠M = 90° (right angle), ∠O = 70° (since the sum of angles in a triangle is 180°).
- One angle is 90°.
- By Angles: Right triangle.
- Sides: LM ≠ MO ≠ LO.
- By Sides: Scalene triangle.

- Triangle ΔOMN:
- Angles: ∠O = 90° (right angle), ∠M = 60°, ∠N = 30° (since the sum of angles in a triangle is 180°).
- One angle is 90°.
- By Angles: Right triangle.
- Sides: OM ≠ MN ≠ ON.
- By Sides: Scalene triangle.

- Triangle ΔLMN:
- Angles: ∠L = 20°, ∠M = 120° (obtuse angle), ∠N = 40° (since the sum of angles in a triangle is 180°).
- One angle is greater than 90°.
- By Angles: Obtuse triangle.
- Sides: LM ≠ MN ≠ LN.
- By Sides: Scalene triangle.

##### Problem 17:
- Triangle ΔEFH:
- Angles: ∠E = 90° (right angle), ∠F = 60°, ∠H = 30° (since the sum of angles in a triangle is 180°).
- One angle is 90°.
- By Angles: Right triangle.
- Sides: EF ≠ FH ≠ EH.
- By Sides: Scalene triangle.

- Triangle ΔEHG:
- Angles: ∠E = 90° (right angle), ∠H = 30°, ∠G = 60° (since the sum of angles in a triangle is 180°).
- One angle is 90°.
- By Angles: Right triangle.
- Sides: EH ≠ HG ≠ EG.
- By Sides: Scalene triangle.

- Triangle ΔEFG:
- Angles: ∠E = 90° (right angle), ∠F = 60°, ∠G = 30° (since the sum of angles in a triangle is 180°).
- One angle is 90°.
- By Angles: Right triangle.
- Sides: EF ≠ FG ≠ EG.
- By Sides: Scalene triangle.

##### Problem 18:
- Triangle ΔXYZ:
- Angles: ∠X = 90° (right angle), ∠Y = 45°, ∠Z = 45° (since the sum of angles in a triangle is 180°).
- One angle is 90°.
- By Angles: Right triangle.
- Sides: XY ≠ YZ ≠ XZ.
- By Sides: Scalene triangle.

- Triangle ΔTUV:
- Angles: ∠T = 75°, ∠U = 75°, ∠V = 30° (since the sum of angles in a triangle is 180°).
- All angles are less than 90°.
- By Angles: Acute triangle.
- Sides: TU = UV ≠ TV.
- By Sides: Isosceles triangle.

- Triangle ΔTSZ:
- Angles: ∠T = 90° (right angle), ∠S = 45°, ∠Z = 45° (since the sum of angles in a triangle is 180°).
- One angle is 90°.
- By Angles: Right triangle.
- Sides: TS ≠ SZ ≠ TZ.
- By Sides: Scalene triangle.

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Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Angles:} \\
1. \text{Acute}, 2. \text{Obtuse}, 3. \text{Acute}, 4. \text{Right}, 5. \text{Acute}, 6. \text{Right}, 7. \text{Obtuse}, 8. \text{Equiangular} \\
\text{Sides:} \\
9. \text{Scalene}, 10. \text{Isosceles}, 11. \text{Scalene}, 12. \text{Isosceles}, 13. \text{Equilateral}, 14. \text{Scalene} \\
\text{Charts: See detailed classifications above.}
\end{array}
}
\]