classify triangles by sides - Free Printable

Problem Analysis:

The task is to classify the given triangles based on their sides and identify which of them are scalene triangles. Let's break this down step by step.

#### Definition of a Scalene Triangle:
A scalene triangle is a triangle in which all three sides have different lengths. In other words, no two sides are equal.

#### Steps to Solve:
1. Identify the side lengths of each triangle.
2. Classify each triangle based on its side lengths:
- Scalene Triangle: All three sides have different lengths.
- Isosceles Triangle: At least two sides are equal.
- Equilateral Triangle: All three sides are equal.
3. Determine which triangles are scalene.

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Classification of Each Triangle:

#### Triangle 1 (NLM):
- Sides: \( NM = 3 \, \text{cm} \), \( ML = 4 \, \text{cm} \), \( LN = 5 \, \text{cm} \)
- All three sides have different lengths.
- Classification: Scalene Triangle

#### Triangle 2 (XYZ):
- Sides: \( XY = 3 \, \text{cm} \), \( YZ = 7 \, \text{cm} \), \( ZX = 3 \, \text{cm} \)
- Two sides are equal (\( XY = ZX = 3 \, \text{cm} \)).
- Classification: Isosceles Triangle

#### Triangle 3 (WXY):
- Sides: \( WX = 7 \, \text{cm} \), \( XY = 2 \, \text{cm} \), \( YW = 4 \, \text{cm} \)
- All three sides have different lengths.
- Classification: Scalene Triangle

#### Triangle 4 (MON):
- Sides: \( MO = 8 \, \text{cm} \), \( ON = 3 \, \text{cm} \), \( NM = 5 \, \text{cm} \)
- All three sides have different lengths.
- Classification: Scalene Triangle

#### Triangle 5 (PQR):
- Sides: \( PQ = 10 \, \text{cm} \), \( QR = 5 \, \text{cm} \), \( RP = 8 \, \text{cm} \)
- All three sides have different lengths.
- Classification: Scalene Triangle

#### Triangle 6 (RST):
- Sides: \( RS = 5 \, \text{cm} \), \( ST = 5 \, \text{cm} \), \( TR = 5 \, \text{cm} \)
- All three sides are equal.
- Classification: Equilateral Triangle

#### Triangle 7 (XYZ):
- Sides: \( XZ = 5 \, \text{cm} \), \( YZ = 5 \, \text{cm} \), \( XY = 5 \, \text{cm} \)
- All three sides are equal.
- Classification: Equilateral Triangle

#### Triangle 8 (ABC):
- Sides: \( AB = 7 \, \text{cm} \), \( BC = 7 \, \text{cm} \), \( CA = 7 \, \text{cm} \)
- All three sides are equal.
- Classification: Equilateral Triangle

#### Triangle 9 (XYZ):
- Sides: \( XY = 7.2 \, \text{cm} \), \( YZ = 7.2 \, \text{cm} \), \( ZX = 7.2 \, \text{cm} \)
- All three sides are equal.
- Classification: Equilateral Triangle

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Final Identification of Scalene Triangles:

From the above classifications, the triangles that are scalene are:
- Triangle 1 (NLM)
- Triangle 3 (WXY)
- Triangle 4 (MON)
- Triangle 5 (PQR)

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Final Answer:

\[
\boxed{\text{Triangles 1, 3, 4, and 5 are scalene triangles.}}
\]