Classifying Triangles Worksheet - Identify right, scalene, isosceles, and equilateral triangles based on side lengths and angles.

To solve the problem of classifying each triangle as right, scalene, isosceles, or equilateral, we need to analyze the properties of each triangle based on their sides and angles. Here's a step-by-step explanation:

Definitions:

1. Right Triangle: A triangle with one angle equal to 90 degrees.
2. Scalene Triangle: A triangle with all three sides of different lengths and all three angles of different measures.
3. Isosceles Triangle: A triangle with at least two sides of equal length (and therefore, at least two angles of equal measure).
4. Equilateral Triangle: A triangle with all three sides of equal length and all three angles equal to 60 degrees.

Analysis of Each Triangle:

#### Triangle 1:
- All sides are marked as unequal.
- No right angle is indicated.
- Classification: Scalene

#### Triangle 2:
- One angle is marked as 90 degrees.
- The other two angles are not equal.
- Classification: Right

#### Triangle 3:
- Two sides are marked as equal.
- No right angle is indicated.
- Classification: Isosceles

#### Triangle 4:
- All sides are marked as unequal.
- No right angle is indicated.
- Classification: Scalene

#### Triangle 5:
- Two sides are marked as equal.
- No right angle is indicated.
- Classification: Isosceles

#### Triangle 6:
- One angle is marked as 90 degrees.
- The other two angles are not equal.
- Classification: Right

#### Triangle 7:
- One angle is marked as 90 degrees.
- The other two angles are not equal.
- Classification: Right

#### Triangle 8:
- Two sides are marked as equal.
- No right angle is indicated.
- Classification: Isosceles

#### Triangle 9:
- One angle is marked as 90 degrees.
- The other two angles are not equal.
- Classification: Right

#### Triangle 10:
- All three sides are marked as equal.
- All three angles are equal (implied by the equal sides).
- Classification: Equilateral

#### Triangle 11:
- All sides are marked as unequal.
- No right angle is indicated.
- Classification: Scalene

#### Triangle 12:
- Two sides are marked as equal.
- No right angle is indicated.
- Classification: Isosceles

Final Classification:

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

Answer:

\[
\boxed{
\text{1. Scalene, 2. Right, 3. Isosceles, 4. Scalene, 5. Isosceles, 6. Right, 7. Right, 8. Isosceles, 9. Right, 10. Equilateral, 11. Scalene, 12. Isosceles}
}
\]