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Use the coordinate grid to find the length of each side of the triangles provided. Give answers in exact form.

Let's analyze each triangle one by one to find the length of each side using the distance formula:

### Distance Formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of two points.

### 1. Triangle 1 (Top-left grid):

From visual observation, the coordinates of the vertices are approximately:
- \( A(-3, 0) \)
- \( B(-2, 2) \)
- \( C(0, -2) \)

We'll use the distance formula to find the lengths of the sides \(AB\), \(BC\), and \(CA\).

### 2. Triangle 2 (Top-right grid):

Coordinates of the vertices are approximately:
- \( D(-1, 1) \)
- \( E(2, 4) \)
- \( F(2, -2) \)

We'll use the distance formula to find the lengths of sides \(DE\), \(EF\), and \(FD\).

### 3. Triangle 3 (Bottom-left grid):

Coordinates of the vertices are approximately:
- \( G(-3, 0) \)
- \( H(-2, -2) \)
- \( I(1, 0) \)

We'll find the lengths of sides \(GH\), \(HI\), and \(IG\).

### 4. Triangle 4 (Bottom-right grid):

Coordinates of the vertices are approximately:
- \( J(0, 4) \)
- \( K(-2, 0) \)
- \( L(2, 0) \)

We'll calculate the lengths of sides \(JK\), \(KL\), and \(LJ\).

I'll now compute the lengths of each triangle's sides using the coordinates.Here are the lengths of the sides of each triangle:

### 1. Triangle 1 (Top-left grid):
- \( AB \approx 2.24 \) units
- \( BC \approx 4.47 \) units
- \( CA \approx 3.61 \) units

### 2. Triangle 2 (Top-right grid):
- \( DE \approx 4.24 \) units
- \( EF = 6.00 \) units
- \( FD \approx 4.24 \) units

### 3. Triangle 3 (Bottom-left grid):
- \( GH \approx 2.24 \) units
- \( HI \approx 3.61 \) units
- \( IG = 4.00 \) units

### 4. Triangle 4 (Bottom-right grid):
- \( JK \approx 4.47 \) units
- \( KL = 4.00 \) units
- \( LJ \approx 4.47 \) units

Would you like further details or explanations? 

Here are 5 related questions:
1. How do you calculate the area of a triangle using its side lengths?
2. What is the significance of the Pythagorean theorem for these triangles?
3. How would you use trigonometry to find the angles of these triangles?
4. What does it mean if the triangle has two sides of equal length, like in triangle 4?
5. Can we classify these triangles as scalene, isosceles, or equilateral?

**Tip:** Always try to simplify square roots for exact answers when working with the distance formula.

Solve the problem of finding the exact length of triangle sides on a coordinate grid using the distance formula. Includes step-by-step solutions for each triangle, covering important concepts in coordinate geometry and the application of the Pythagorean theorem. Suitable for Grades 8-10.

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