Problem Analysis:
The worksheet asks us to classify triangles based on two criteria:
1.
Types of Triangles by Side Lengths:
-
Scalene Triangle: All sides have different lengths.
-
Isosceles Triangle: At least two sides are equal.
-
Equilateral Triangle: All three sides are equal.
2.
Types of Triangles by Angles:
-
Acute Triangle: All angles are less than 90°.
-
Right Triangle: One angle is exactly 90°.
-
Obtuse Triangle: One angle is greater than 90°.
Solution:
#### Part 1: Classify Triangles by Side Lengths
1.
Triangle ABC:
- Sides: \( AB = 5 \, \text{cm} \), \( BC = 4 \, \text{cm} \), \( AC = 4.2 \, \text{cm} \)
- All sides are different.
-
Classification: Scalene Triangle
2.
Triangle PQR:
- Sides: \( PQ = 6 \, \text{cm} \), \( QR = 8 \, \text{cm} \), \( PR = 6 \, \text{cm} \)
- Two sides are equal (\( PQ = PR \)).
-
Classification: Isosceles Triangle
3.
Triangle XYZ:
- Sides: \( XY = 8 \, \text{cm} \), \( YZ = 8 \, \text{cm} \), \( XZ = 8 \, \text{cm} \)
- All sides are equal.
-
Classification: Equilateral Triangle
4.
Triangle UVW:
- Sides: \( UV = 7 \, \text{cm} \), \( VW = 8 \, \text{cm} \), \( UW = 4 \, \text{cm} \)
- All sides are different.
-
Classification: Scalene Triangle
5.
Triangle LMN:
- Sides: \( LM = 3 \, \text{cm} \), \( MN = 6.2 \, \text{cm} \), \( LN = 6.2 \, \text{cm} \)
- Two sides are equal (\( MN = LN \)).
-
Classification: Isosceles Triangle
#### Part 2: Classify Triangles by Angles
1.
Triangle with \( 90^\circ \) Angle:
- One angle is exactly 90°.
-
Classification: Right Triangle
2.
Triangle with \( 120^\circ \) Angle:
- One angle is greater than 90°.
-
Classification: Obtuse Triangle
3.
Triangle with Angles \( 70^\circ \), \( 60^\circ \), and \( 50^\circ \):
- All angles are less than 90°.
-
Classification: Acute Triangle
4.
Triangle with \( 90^\circ \) Angle:
- One angle is exactly 90°.
-
Classification: Right Triangle
5.
Triangle with \( 110^\circ \) Angle:
- One angle is greater than 90°.
-
Classification: Obtuse Triangle
Final Answer:
#### Part 1: Classification by Side Lengths
1. Triangle ABC:
Scalene
2. Triangle PQR:
Isosceles
3. Triangle XYZ:
Equilateral
4. Triangle UVW:
Scalene
5. Triangle LMN:
Isosceles
#### Part 2: Classification by Angles
1. Triangle with \( 90^\circ \):
Right
2. Triangle with \( 120^\circ \):
Obtuse
3. Triangle with \( 70^\circ, 60^\circ, 50^\circ \):
Acute
4. Triangle with \( 90^\circ \):
Right
5. Triangle with \( 110^\circ \):
Obtuse
\[
\boxed{
\begin{array}{ll}
\text{Part 1:} & \text{Scalene, Isosceles, Equilateral, Scalene, Isosceles} \\
\text{Part 2:} & \text{Right, Obtuse, Acute, Right, Obtuse}
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of properties of triangles worksheet.
