Classify triangles by their sides: identify scalene, isosceles, and equilateral triangles based on given side lengths.

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.
Additionally, all three angles are also different.

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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Now, let’s classify each triangle in the image based on their side lengths.

We'll go through each triangle one by one.

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✔ Triangle 1: ΔNML

- Sides: 5 cm, 4 cm, 3 cm
- All sides are different → Scalene

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✔ Triangle 2: ΔZXY

- Sides: 7 cm, 3 cm, 3 cm
- Two sides are equal (3 cm) → Isosceles

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✔ Triangle 3: ΔYWX

- Sides: 7 cm, 4 cm, 2 cm
- All sides are different → Scalene

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✔ Triangle 4: ΔOMN

- Sides: 8 cm, 5 cm, 3 cm
- All sides are different → Scalene

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✔ Triangle 5: ΔQPR

- Sides: 10 cm, 8 cm, 5 cm
- All sides are different → Scalene

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✔ Triangle 6: ΔSRT

- Sides: 5 cm, 5 cm, 5 cm
- All sides are equal → Equilateral

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✔ Triangle 7: ΔYZX

- Sides: 5 cm, 5 cm, and the hypotenuse (not labeled directly, but it's a right triangle with two legs = 5 cm)
- Since two sides are equal (5 cm), even if the third is different → Isosceles

> Note: This is a right triangle with legs of 5 cm each, so it's an isosceles right triangle.

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✔ Triangle 8: ΔABC

- Sides: 7 cm, 7 cm, and base not labeled, but from diagram, AB = BC = 7 cm
- So two sides are equal → Isosceles

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✔ Triangle 9: ΔXYZ

- Sides: 7.2 cm, 7.2 cm, 7.2 cm
- All sides equal → Equilateral

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📊 Final Classification:

| Triangle | Side Lengths | Type |
|--------|--------------|------|
| 1 (ΔNML) | 5, 4, 3 | Scalene |
| 2 (ΔZXY) | 7, 3, 3 | Isosceles |
| 3 (ΔYWX) | 7, 4, 2 | Scalene |
| 4 (ΔOMN) | 8, 5, 3 | Scalene |
| 5 (ΔQPR) | 10, 8, 5 | Scalene |
| 6 (ΔSRT) | 5, 5, 5 | Equilateral |
| 7 (ΔYZX) | 5, 5, ? | Isosceles |
| 8 (ΔABC) | 7, 7, ? | Isosceles |
| 9 (ΔXYZ) | 7.2, 7.2, 7.2 | Equilateral |

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✔ Summary:

- Scalene Triangles: 1, 3, 4, 5
- Isosceles Triangles: 2, 7, 8
- Equilateral Triangles: 6, 9

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✔ Answer to "What is a scalene triangle?"

> A scalene triangle is a triangle in which all three sides have different lengths.

And based on the classification:
- The scalene triangles in the image are: ΔNML, ΔYWX, ΔOMN, ΔQPR

Let me know if you'd like this summarized visually!