Question
Omplete the condition stetment that must be met in order for three side lenghts a , b , and c to be a rroangle
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GPT-4o mini
To determine whether three side lengths \( a \), \( b \), and \( c \) can form a triangle, they must satisfy the Triangle Inequality Theorem, which states:
1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)
If you specifically want to know about a right triangle, in addition to the Triangle Inequality, the Pythagorean theorem must be satisfied. For side lengths \( a \), \( b \), and \( c \) (where \( c \) is the longest side), the condition for them to form a right triangle is:
\[ a^2 + b^2 = c^2 \]
This means that the square of the length of the longest side must equal the sum of the squares of the other two sides.
1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)
If you specifically want to know about a right triangle, in addition to the Triangle Inequality, the Pythagorean theorem must be satisfied. For side lengths \( a \), \( b \), and \( c \) (where \( c \) is the longest side), the condition for them to form a right triangle is:
\[ a^2 + b^2 = c^2 \]
This means that the square of the length of the longest side must equal the sum of the squares of the other two sides.