Identifying types of triangles worksheet for geometry practice.

To solve the problem of identifying the type of each triangle as equilateral, isosceles, or scalene, we need to analyze the lengths of the sides of each triangle. Here's a step-by-step explanation:

Definitions:

1. Equilateral Triangle: All three sides are equal.
2. Isosceles Triangle: At least two sides are equal.
3. Scalene Triangle: All three sides are different.

Analysis of Each Triangle:

#### Solved Example:
- Triangle 0 (Given in the solved section):
- Sides: \(a = a = a\)
- Type: Equilateral Triangle

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#### Triangles 1 to 11:

1. Triangle 1:
- Sides: \(a, b, c\) (all different)
- Type: Scalene Triangle

2. Triangle 2:
- Sides: \(a, b, c\) (two sides labeled \(a\) and \(b\), one side \(c\))
- Type: Isosceles Triangle (since \(a = b\))

3. Triangle 3:
- Sides: \(p, p, q\) (two sides labeled \(p\), one side \(q\))
- Type: Isosceles Triangle (since \(p = p\))

4. Triangle 4:
- Sides: \(p, p, r\) (two sides labeled \(p\), one side \(r\))
- Type: Isosceles Triangle (since \(p = p\))

5. Triangle 5:
- Sides: \(p, q, r\) (all different)
- Type: Scalene Triangle

6. Triangle 6:
- Sides: \(x, x, y\) (two sides labeled \(x\), one side \(y\))
- Type: Isosceles Triangle (since \(x = x\))

7. Triangle 7:
- Sides: \(x, x, x\) (all sides labeled \(x\))
- Type: Equilateral Triangle (since \(x = x = x\))

8. Triangle 8:
- Sides: \(p, q, s\) (all different)
- Type: Scalene Triangle

9. Triangle 9:
- Sides: \(p, g, q\) (all different)
- Type: Scalene Triangle

10. Triangle 10:
- Sides: \(x, z, a\) (all different)
- Type: Scalene Triangle

11. Triangle 11:
- Sides: \(m, n, p\) (all different)
- Type: Scalene Triangle

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Final Answer:

\[
\boxed{
\begin{array}{ll}
1 & \text{Scalene} \\
2 & \text{Isosceles} \\
3 & \text{Isosceles} \\
4 & \text{Isosceles} \\
5 & \text{Scalene} \\
6 & \text{Isosceles} \\
7 & \text{Equilateral} \\
8 & \text{Scalene} \\
9 & \text{Scalene} \\
10 & \text{Scalene} \\
11 & \text{Scalene} \\
\end{array}
}
\]