Question
Is the triangle formed a right triangle? If it is, select all that applies. If not, select "Not a right triangle".
A It's a right triangle because 3 + 5²=6
B It's a right triangle because 9 +25 equals 36
C It's a right triangle because a² + b² = c
D Not a right triangle
E It's a right triangle because there's a 90-degree angle
F It's right triangle because the legs are on the right side
(It is a right triangle)
Choose all that are true
A It's a right triangle because 3 + 5²=6
B It's a right triangle because 9 +25 equals 36
C It's a right triangle because a² + b² = c
D Not a right triangle
E It's a right triangle because there's a 90-degree angle
F It's right triangle because the legs are on the right side
(It is a right triangle)
Choose all that are true
Answers
GPT-4o mini
To determine if the triangle is a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the equation \(a^2 + b^2 = c^2\) must hold true.
Let's analyze each option:
A. **It's a right triangle because 3 + 5²=6**: This statement is incorrect. \(3 + 5^2 = 3 + 25 = 28\), which does not equal 6.
B. **It's a right triangle because 9 + 25 equals 36**: This statement is correct. If we interpret \(9\) as \(3^2\) and \(25\) as \(5^2\), then \(3^2 + 5^2 = 9 + 25 = 36\), which is \(6^2\). This satisfies the Pythagorean theorem, indicating a right triangle.
C. **It's a right triangle because a² + b² = c**: This statement is incorrect. The correct relationship should be \(a^2 + b^2 = c^2\), not \(c\).
D. **Not a right triangle**: This option is incorrect since we have established that it is a right triangle.
E. **It's a right triangle because there's a 90-degree angle**: This statement is valid since the definition of a right triangle includes having a 90-degree angle.
F. **It's a right triangle because the legs are on the right side**: This statement is subjective and does not provide a valid mathematical justification for a right triangle.
Based on the analysis, the true statements are:
- B (It’s a right triangle because 9 + 25 equals 36)
- E (It’s a right triangle because there’s a 90-degree angle)
So the correct selections are **B** and **E**.
Let's analyze each option:
A. **It's a right triangle because 3 + 5²=6**: This statement is incorrect. \(3 + 5^2 = 3 + 25 = 28\), which does not equal 6.
B. **It's a right triangle because 9 + 25 equals 36**: This statement is correct. If we interpret \(9\) as \(3^2\) and \(25\) as \(5^2\), then \(3^2 + 5^2 = 9 + 25 = 36\), which is \(6^2\). This satisfies the Pythagorean theorem, indicating a right triangle.
C. **It's a right triangle because a² + b² = c**: This statement is incorrect. The correct relationship should be \(a^2 + b^2 = c^2\), not \(c\).
D. **Not a right triangle**: This option is incorrect since we have established that it is a right triangle.
E. **It's a right triangle because there's a 90-degree angle**: This statement is valid since the definition of a right triangle includes having a 90-degree angle.
F. **It's a right triangle because the legs are on the right side**: This statement is subjective and does not provide a valid mathematical justification for a right triangle.
Based on the analysis, the true statements are:
- B (It’s a right triangle because 9 + 25 equals 36)
- E (It’s a right triangle because there’s a 90-degree angle)
So the correct selections are **B** and **E**.