Classifying Triangles Worksheet - Identify types of triangles based on angles and side lengths.

Let’s go step by step through each problem on the worksheet.

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Part 1: Classify each triangle as right, acute, or obtuse.

We use angle measures to classify:

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

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Problem 1:
Angles: 55°, 90°, and we can find the third:
180° - 55° - 90° = 35°
→ Has a 90° angle → Right

Problem 2:
Angles: 40°, 60°, so third = 180 - 40 - 60 = 80°
All angles < 90° → Acute

Problem 3:
Angles: 120°, 30°, so third = 180 - 120 - 30 = 30°
Has an angle > 90° (120°) → Obtuse

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Part 2: Find the value of x (the measure of the third angle).

Remember: Sum of angles in any triangle = 180°

Problem 4:
Angles: 120°, 30°, so x = 180 - 120 - 30 = 30°

Problem 5:
Angles: 60°, 60°, so x = 180 - 60 - 60 = 60°

Problem 6:
Right triangle → one angle is 90°, another is 40°, so x = 180 - 90 - 40 = 50°

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Part 3: Classify each triangle as equilateral, isosceles, or scalene.

Definitions:

- Equilateral: All three sides equal (also all angles 60°).
- Isosceles: At least two sides equal.
- Scalene: All sides different.

Look at side markings — tick marks mean those sides are equal.

Problem 7:
Sides: 7, 12, 9 — no equal sides → Scalene

Problem 8:
Two sides have single tick marks → two sides equal → Isosceles

Problem 9:
Sides: 9, 8, 10 — all different → Scalene

Problem 10:
All three sides have same tick mark → all sides equal → Equilateral

Problem 11:
Base angles both 40° → if two angles are equal, then the sides opposite them are equal → Isosceles

Problem 12:
Angles: 100°, 40°, so third = 180 - 100 - 40 = 40°
Two angles equal (40°, 40°) → sides opposite them equal → Isosceles

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✔ All answers verified.

Final Answer:
1. Right
2. Acute
3. Obtuse
4. 30°
5. 60°
6. 50°
7. Scalene
8. Isosceles
9. Scalene
10. Equilateral
11. Isosceles
12. Isosceles