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
FIt's a right triangle because the legs are on the right side
(It is 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
FIt's a right triangle because the legs are on the right side
(It is a right triangle)
Answers
GPT-4o mini
To determine if a triangle is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). We will evaluate the given options:
A) **It's a right triangle because 3 + 5² = 6**
This statement is incorrect because \(3 + 5^2 = 3 + 25 = 28\), which does not equal 6.
B) **It's a right triangle because 9 + 25 equals 36**
This implies \(9 + 25 = 36\), which could be interpreted as \(3^2 + 5^2 = 6^2\) (where 3 and 5 are legs, and 6 is the hypotenuse). This is correct, so it suggests that it could potentially be a right triangle.
C) **It's a right triangle because a² + b² = c**
This is not the correct form of the Pythagorean theorem, which is \(a^2 + b^2 = c^2\). Hence, this statement is misleading.
D) **Not a right triangle**
This depends on the evaluations above. If B stands true, then this option is incorrect.
E) **It's a right triangle because there's a 90-degree angle**
If a triangle has a 90-degree angle, it is definitively a right triangle. If triangles are mentioned to have such angles, that would make it a right triangle.
F) **It's a right triangle because the legs are on the right side**
This statement is unclear. The positioning of legs doesn't determine whether a triangle is a right triangle.
Given the evaluations, the correct selections based on the logic presented are:
**B** (assuming they are referring to \(3^2 + 5^2 = 6^2\)) and **E** (if there is indeed a 90-degree angle).
Thus, it can correctly be confirmed that the triangle is a right triangle based on the justification provided and options available.
A) **It's a right triangle because 3 + 5² = 6**
This statement is incorrect because \(3 + 5^2 = 3 + 25 = 28\), which does not equal 6.
B) **It's a right triangle because 9 + 25 equals 36**
This implies \(9 + 25 = 36\), which could be interpreted as \(3^2 + 5^2 = 6^2\) (where 3 and 5 are legs, and 6 is the hypotenuse). This is correct, so it suggests that it could potentially be a right triangle.
C) **It's a right triangle because a² + b² = c**
This is not the correct form of the Pythagorean theorem, which is \(a^2 + b^2 = c^2\). Hence, this statement is misleading.
D) **Not a right triangle**
This depends on the evaluations above. If B stands true, then this option is incorrect.
E) **It's a right triangle because there's a 90-degree angle**
If a triangle has a 90-degree angle, it is definitively a right triangle. If triangles are mentioned to have such angles, that would make it a right triangle.
F) **It's a right triangle because the legs are on the right side**
This statement is unclear. The positioning of legs doesn't determine whether a triangle is a right triangle.
Given the evaluations, the correct selections based on the logic presented are:
**B** (assuming they are referring to \(3^2 + 5^2 = 6^2\)) and **E** (if there is indeed a 90-degree angle).
Thus, it can correctly be confirmed that the triangle is a right triangle based on the justification provided and options available.