Classify triangles by their sides: scalene, isosceles, and equilateral.

Let's solve the problem step by step.

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🔹 What is a Scalene Triangle?

A scalene triangle is a triangle in which all three sides have different lengths.
This means:
- No two sides are equal.
- All angles are also different (since side lengths determine angles).

There are three types of triangles based on their sides:

1. Scalene triangle: All sides are different.
2. Isosceles triangle: Two sides are equal.
3. Equilateral triangle: All three sides are equal.

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🔹 Task: Classify the triangles by their sides

We are given 9 triangles with side lengths labeled. Let’s analyze each one.

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#### ✔ Triangle 1: ΔNLM
- Sides: 5 cm, 4 cm, 3 cm
- All sides are different → Scalene

#### ✔ Triangle 2: ΔZXY
- Sides: 7 cm, 3 cm, 3 cm
- Two sides are equal (3 cm) → Isosceles

#### ✔ Triangle 3: ΔYWX
- Sides: 7 cm, 4 cm, 2 cm
- All sides different → Scalene

#### ✔ Triangle 4: ΔOMN
- Sides: 8 cm, 5 cm, 3 cm
- All sides different → Scalene

#### ✔ Triangle 5: ΔPQR
- Sides: 10 cm, 8 cm, 5 cm
- All sides different → Scalene

#### ✔ Triangle 6: ΔRST
- Sides: 5 cm, 5 cm, 5 cm
- All sides equal → Equilateral

#### ✔ Triangle 7: ΔXYZ
- Sides: 5 cm, 5 cm, 5 cm (wait — let's check)
- YX = 5 cm
- YZ = 5 cm
- XZ = ?
- But we see it's a right triangle with legs 5 cm and 5 cm → hypotenuse would be √(5² + 5²) = √50 ≈ 7.07 cm
- But in the diagram, only two sides are labeled as 5 cm → third side not labeled?
- Wait: Actually, from the image:
- YX = 5 cm
- YZ = 5 cm
- And angle at Y is right angle → So it's an isosceles right triangle
- Therefore, two sides equal → Isosceles

> Note: Even though the third side isn't labeled, we can deduce it's different (≈7.07), so two sides equal → Isosceles

#### ✔ Triangle 8: ΔABC
- Sides: AB = 7 cm, BC = 7 cm, AC = ?
- But only two sides labeled: AB = 7 cm, BC = 7 cm
- Third side not labeled, but since two sides are equal → Isosceles

> Even without knowing the third side, if two are equal, it's isosceles.

#### ✔ Triangle 9: ΔXYZ (last one)
- Sides: XY = 7.2 cm, XZ = 7.2 cm, YZ = 7.2 cm
- All sides are 7.2 cm → Equilateral

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🔸 Summary of Classification:

| Triangle | Side Lengths | Type |
|--------|--------------------------|--------------|
| 1 (NLM) | 5, 4, 3 | Scalene |
| 2 (ZXY) | 7, 3, 3 | Isosceles |
| 3 (YWX) | 7, 4, 2 | Scalene |
| 4 (OMN) | 8, 5, 3 | Scalene |
| 5 (PQR) | 10, 8, 5 | Scalene |
| 6 (RST) | 5, 5, 5 | Equilateral |
| 7 (XYZ) | 5, 5, ? (right triangle) | Isosceles |
| 8 (ABC) | 7, 7, ? | Isosceles |
| 9 (XYZ) | 7.2, 7.2, 7.2 | Equilateral |

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✔ Final Answer:

Classify the triangles by their sides:

- Scalene Triangles: 1 (NLM), 3 (YWX), 4 (OMN), 5 (PQR)
- Isosceles Triangles: 2 (ZXY), 7 (XYZ), 8 (ABC)
- Equilateral Triangles: 6 (RST), 9 (XYZ)

> Note: Triangle 7 and 8 are isosceles because they have two equal sides (even if the third side is unknown or not labeled, the presence of two equal sides defines them as isosceles).

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🟩 What is a scalene triangle?

> A scalene triangle is a triangle in which all three sides have different lengths, and consequently, all three angles are also different.

✔ Example: Triangle NLM (5 cm, 4 cm, 3 cm) is scalene.

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Let me know if you'd like this summarized in a table format!