Classify triangles by angles and sides in this geometry worksheet.

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°).
- 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° (sum of angles in a triangle is 180°).
- All angles are less than 90°.
- By Angles: Acute
- Sides: AB ≠ BD ≠ AD.
- By Sides: Scalene

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

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

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

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

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

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

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

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

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

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

- Triangle ΔTSZ:
- Angles: ∠T = 120° (obtuse angle), ∠S = 30°, ∠Z = 30° (sum of angles in a triangle is 180°).
- One angle is greater than 90°.
- By Angles: Obtuse
- Sides: TS ≠ SZ ≠ TZ.
- By Sides: Scalene

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Final Answer:

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