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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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°).
- Sides: AB ≠ BD ≠ AD.
- Classification by Angles: Acute
- Classification by Sides: Scalene

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

- Triangle ΔABC:
- Angles: ∠A = 55°, ∠B = 70°, ∠C = 55° (since the sum of angles in a triangle is 180°).
- Sides: AB = AC ≠ BC.
- Classification by Angles: Acute
- Classification by Sides: Isosceles

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

- Triangle ΔOMN:
- Angles: ∠O = 90°, ∠M = 45°, ∠N = 45° (since the sum of angles in a triangle is 180°).
- Sides: OM = ON ≠ MN.
- Classification by Angles: Right
- Classification by Sides: Isosceles

- Triangle ΔLMN:
- Angles: ∠L = 20°, ∠M = 135°, ∠N = 25° (since the sum of angles in a triangle is 180°).
- Sides: LM ≠ MN ≠ LN.
- Classification by Angles: Obtuse
- Classification by Sides: Scalene

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

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

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

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

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

- Triangle ΔTSZ:
- Angles: ∠T = 120°, ∠S = 30°, ∠Z = 30° (since the sum of angles in a triangle is 180°).
- Sides: TS ≠ SZ ≠ TZ.
- Classification by Angles: Obtuse
- Classification by Sides: Scalene

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Final Answer:

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