Problem Overview:
The task involves classifying triangles based on two criteria:
1.
By Sides: Equilateral, Isosceles, or Scalene.
2.
By Angles: Acute, Right, or Obtuse.
We will analyze each triangle in the image and classify them accordingly.
---
Part 1: Classifying Triangles by Sides
#### Definitions:
-
Equilateral Triangle: All three sides are equal.
-
Isosceles Triangle: At least two sides are equal.
-
Scalene Triangle: No sides are equal.
#### Analysis of Each Triangle:
1.
Triangle 1:
- Sides: None of the sides appear to be equal.
- Classification:
Scalene
2.
Triangle 2:
- Sides: Two sides are marked as equal (indicated by the same symbol).
- Classification:
Isosceles
3.
Triangle 3:
- Sides: None of the sides appear to be equal.
- Classification:
Scalene
4.
Triangle 4:
- Sides: Two sides are marked as equal (indicated by the same symbol).
- Classification:
Isosceles
5.
Triangle 5:
- Sides: All three sides are marked as equal (indicated by the same symbol).
- Classification:
Equilateral
6.
Triangle 6:
- Sides: None of the sides appear to be equal.
- Classification:
Scalene
---
Part 2: Classifying Triangles by Angles
#### Definitions:
-
Acute Triangle: All angles are less than 90°.
-
Right Triangle: One angle is exactly 90°.
-
Obtuse Triangle: One angle is greater than 90°.
#### Analysis of Each Triangle:
7.
Triangle 7:
- Angles: One angle appears to be greater than 90°.
- Classification:
Obtuse
8.
Triangle 8:
- Angles: All angles appear to be less than 90°.
- Classification:
Acute
9.
Triangle 9:
- Angles: One angle is exactly 90° (right angle).
- Classification:
Right
10.
Triangle 10:
- Angles: One angle appears to be greater than 90°.
- Classification:
Obtuse
11.
Triangle 11:
- Angles: One angle is exactly 90° (right angle).
- Classification:
Right
12.
Triangle 12:
- Angles: All angles appear to be less than 90°.
- Classification:
Acute
---
Final Answer:
#### By Sides:
1. Scalene
2. Isosceles
3. Scalene
4. Isosceles
5. Equilateral
6. Scalene
#### By Angles:
7. Obtuse
8. Acute
9. Right
10. Obtuse
11. Right
12. Acute
Boxed Answer:
\[
\boxed{
\begin{array}{ccc}
\text{By Sides:} & \text{By Angles:} \\
1. \text{Scalene} & 7. \text{Obtuse} \\
2. \text{Isosceles} & 8. \text{Acute} \\
3. \text{Scalene} & 9. \text{Right} \\
4. \text{Isosceles} & 10. \text{Obtuse} \\
5. \text{Equilateral} & 11. \text{Right} \\
6. \text{Scalene} & 12. \text{Acute} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of identifying types of triangles worksheet.
