A triangular sail has side lengths of 9 meters, 40 meters, and 41 meters. Does this sail form a right triangle?

Yes, because $9^2 + 40^2 = 41^2$.

No, because $9^2 + 40^2 \neq 41^2$.

A rectangular gate is braced with a diagonal piece of wood. The gate's width is 20 inches and its height is 21 inches. If the diagonal brace is 29 inches long, does the gate form a right angle?

Yes, the corner is a right angle.

No, the corner is not a right angle.

Yes, because the sides are integers.

Understand the Converse of the Pythagorean Theorem Practice — Grade 8 math

Lesson 2: Understand the Converse of the Pythagorean Theorem — Practice Questions

1. A triangular sail has side lengths of 9 meters, 40 meters, and 41 meters. Does this sail form a right triangle?
- A. Yes, because $9^2 + 40^2 = 41^2$.
- B. No, because $9^2 + 40^2 \neq 41^2$.
- C. Yes, because $9 + 40 > 41$.
- D. Cannot be determined.
2. A triangle has side lengths of 10 cm, 11 cm, and 14 cm. To check if it's a right triangle, we compare $10^2 + 11^2$ with $14^2$. What is the value of $10^2 + 11^2$? ___
3. A rectangular gate is braced with a diagonal piece of wood. The gate's width is 20 inches and its height is 21 inches. If the diagonal brace is 29 inches long, does the gate form a right angle?
- A. Yes, the corner is a right angle.
- B. No, the corner is not a right angle.
- C. It is impossible to know.
- D. Yes, because the sides are integers.
4. A triangle has side lengths of 5 units, 8 units, and $\sqrt{39}$ units. Is this a right triangle? Answer Yes or No. ___
5. A plot of land is a triangle with side lengths of $\frac{8}{15}$ miles, 1 mile, and $\frac{17}{15}$ miles. Is it a right-angled plot? Answer Yes or No. ___
6. A triangular garden plot has side lengths of 10 feet, 11 feet, and 12 feet. What type of triangle is formed by the garden plot's borders?
- A. Acute
- B. Obtuse
- C. Right
- D. Not a triangle
7. A craftsman is building a triangular frame with wooden beams measuring 6 meters, 9 meters, and 13 meters. How would you classify this triangle?
- A. Obtuse
- B. Acute
- C. Right
- D. Isosceles
8. The three sides of a triangular park measure 8 miles, 15 miles, and 17 miles. What is the correct classification for this park?
- A. Right
- B. Acute
- C. Obtuse
- D. Cannot be determined
9. To classify a triangle with sides 4, 7, and 8, you compare $4^2 + 7^2$ with $8^2$. What is the value of $4^2 + 7^2$? ___
10. A triangle has side lengths of 5 cm, 6 cm, and $\sqrt{50}$ cm. How would you classify this triangle?
- A. Acute
- B. Obtuse
- C. Right
- D. Equilateral