3rd Grade Geometry Worksheets - Free Printable

To classify the triangles in the given worksheet, we need to analyze each triangle based on its side lengths and angles. Here's a step-by-step explanation for each triangle:

Triangle 1:

- Side lengths: 3 cm, 4 cm, 5 cm
- Classification:
- Equilateral: No, because all sides are not equal.
- Isosceles: No, because no two sides are equal.
- Scalene: Yes, because all sides are different.
- Right: Yes, because it satisfies the Pythagorean theorem: \(3^2 + 4^2 = 5^2\) (9 + 16 = 25).
- Acute: No, because it is a right triangle.
- Obtuse: No, because it is a right triangle.

Final Classification: Scalene, Right

Triangle 2:

- Side lengths: 8 in, 8 in, 5 in
- Classification:
- Equilateral: No, because not all sides are equal.
- Isosceles: Yes, because two sides are equal (8 in, 8 in).
- Scalene: No, because it is isosceles.
- Right: No, because it does not satisfy the Pythagorean theorem: \(8^2 + 5^2 \neq 8^2\) (64 + 25 ≠ 64).
- Acute: Yes, because all angles are less than 90 degrees (can be verified using the cosine rule or by noting that the longest side is shorter than what would be required for a right triangle).
- Obtuse: No, because it is acute.

Final Classification: Isosceles, Acute

Triangle 3:

- Side lengths: 6 in, 7 in, 8 in
- Classification:
- Equilateral: No, because not all sides are equal.
- Isosceles: No, because no two sides are equal.
- Scalene: Yes, because all sides are different.
- Right: No, because it does not satisfy the Pythagorean theorem: \(6^2 + 7^2 \neq 8^2\) (36 + 49 ≠ 64).
- Acute: Yes, because all angles are less than 90 degrees (can be verified using the cosine rule).
- Obtuse: No, because it is acute.

Final Classification: Scalene, Acute

Triangle 4:

- Side lengths: 4 cm, 4 cm, 4 cm
- Classification:
- Equilateral: Yes, because all sides are equal.
- Isosceles: Yes, because all sides are equal (technically, an equilateral triangle is also isosceles).
- Scalene: No, because it is equilateral.
- Right: No, because it cannot have a right angle (all angles are 60 degrees).
- Acute: Yes, because all angles are less than 90 degrees.
- Obtuse: No, because it is acute.

Final Classification: Equilateral, Acute

Triangle 5:

- Side lengths: 4 m, 6 m, 8 m
- Classification:
- Equilateral: No, because not all sides are equal.
- Isosceles: No, because no two sides are equal.
- Scalene: Yes, because all sides are different.
- Right: No, because it does not satisfy the Pythagorean theorem: \(4^2 + 6^2 \neq 8^2\) (16 + 36 ≠ 64).
- Acute: No, because the square of the longest side is greater than the sum of the squares of the other two sides, indicating an obtuse angle.
- Obtuse: Yes, because \(4^2 + 6^2 < 8^2\) (16 + 36 < 64).

Final Classification: Scalene, Obtuse

Summary of Classifications:

| Triangle | Equilateral | Isosceles | Scalene | Right | Acute | Obtuse |
|----------|-------------|-----------|---------|-------|-------|--------|
| 1 | | | √ | √ | | |
| 2 | | √ | | | √ | |
| 3 | | | √ | | √ | |
| 4 | √ | √ | | | √ | |
| 5 | | | √ | | | √ |

Final Answer:

\[
\boxed{
\begin{array}{c|c|c|c|c|c|c}
\text{Triangle} & \text{Equilateral} & \text{Isosceles} & \text{Scalene} & \text{Right} & \text{Acute} & \text{Obtuse} \\
\hline
1 & & & \checkmark & \checkmark & & \\
2 & & \checkmark & & & \checkmark & \\
3 & & & \checkmark & & \checkmark & \\
4 & \checkmark & \checkmark & & & \checkmark & \\
5 & & & \checkmark & & & \checkmark \\
\end{array}
}
\]