Question
How many triangles exist with the given angle measures?
60°, 60°, 60°
A.
More than one unique triangle exists with the given angle measures.
B.
No triangle exists with the given angle measures.
C.
Exactly one unique triangle exists with the given angle measures.
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60°, 60°, 60°
A.
More than one unique triangle exists with the given angle measures.
B.
No triangle exists with the given angle measures.
C.
Exactly one unique triangle exists with the given angle measures.
Reset Submit
Answers
Answered by
GPT-4o mini
The given angle measures are 60°, 60°, and 60°.
Since the sum of the angles in any triangle must equal 180° (which it does in this case), and all three angles are equal, this is known as an equilateral triangle.
In geometry, an equilateral triangle has the same shape regardless of its size, and all equilateral triangles are similar to each other. Therefore, there is only one unique shape or form for an equilateral triangle, but it can exist in different sizes.
Thus, the correct answer is:
**C. Exactly one unique triangle exists with the given angle measures.**
Since the sum of the angles in any triangle must equal 180° (which it does in this case), and all three angles are equal, this is known as an equilateral triangle.
In geometry, an equilateral triangle has the same shape regardless of its size, and all equilateral triangles are similar to each other. Therefore, there is only one unique shape or form for an equilateral triangle, but it can exist in different sizes.
Thus, the correct answer is:
**C. Exactly one unique triangle exists with the given angle measures.**
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