Question
Carrie is asked to draw a triangle with the following specification.
at least two angles measuring 60°
Which of the following statements about this triangle is true?
A.
One and only one triangle exists with the given condition, and it must be an equilateral triangle.
B.
More than one triangle exists with the given condition, and all instances must be isosceles triangles.
C.
More than one triangle exists with the given condition, and all instances must be equilateral triangles.
D.
One and only one triangle exists with the given condition, and it must be an isosceles triangle.
at least two angles measuring 60°
Which of the following statements about this triangle is true?
A.
One and only one triangle exists with the given condition, and it must be an equilateral triangle.
B.
More than one triangle exists with the given condition, and all instances must be isosceles triangles.
C.
More than one triangle exists with the given condition, and all instances must be equilateral triangles.
D.
One and only one triangle exists with the given condition, and it must be an isosceles triangle.
Answers
GPT-4o mini
To analyze the given specifications—specifically, that the triangle has at least two angles measuring 60°—we can draw the following conclusions:
1. If a triangle has two angles measuring 60°, the sum of the angles in any triangle is 180°. Therefore, the third angle must measure \( 180° - (60° + 60°) = 60° \) as well.
2. This means that all three angles of the triangle measure 60°. A triangle with all angles equal to 60° is an equilateral triangle.
So, according to the specifications, the only triangle that satisfies the condition of having at least two angles of 60° is an equilateral triangle.
Now, let's evaluate the statements:
- **A.** One and only one triangle exists with the given condition, and it must be an equilateral triangle. (True)
- **B.** More than one triangle exists with the given condition, and all instances must be isosceles triangles. (False)
- **C.** More than one triangle exists with the given condition, and all instances must be equilateral triangles. (False)
- **D.** One and only one triangle exists with the given condition, and it must be an isosceles triangle. (False)
The correct answer is **A**: One and only one triangle exists with the given condition, and it must be an equilateral triangle.
1. If a triangle has two angles measuring 60°, the sum of the angles in any triangle is 180°. Therefore, the third angle must measure \( 180° - (60° + 60°) = 60° \) as well.
2. This means that all three angles of the triangle measure 60°. A triangle with all angles equal to 60° is an equilateral triangle.
So, according to the specifications, the only triangle that satisfies the condition of having at least two angles of 60° is an equilateral triangle.
Now, let's evaluate the statements:
- **A.** One and only one triangle exists with the given condition, and it must be an equilateral triangle. (True)
- **B.** More than one triangle exists with the given condition, and all instances must be isosceles triangles. (False)
- **C.** More than one triangle exists with the given condition, and all instances must be equilateral triangles. (False)
- **D.** One and only one triangle exists with the given condition, and it must be an isosceles triangle. (False)
The correct answer is **A**: One and only one triangle exists with the given condition, and it must be an equilateral triangle.