Question
In right triangle RST, ST = 5, RT = 12, and RS = 13.
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GPT 3.5
To determine if triangle RST is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the sides of triangle RST are ST = 5, RT = 12, and RS = 13. Let's calculate the square of the length of each side:
ST^2 = 5^2 = 25
RT^2 = 12^2 = 144
RS^2 = 13^2 = 169
Now, let's check if the Pythagorean theorem holds:
13^2 = 169
5^2 + 12^2 = 25 + 144 = 169
Since the square of the length of the hypotenuse (RS) is equal to the sum of the squares of the lengths of the other two sides (ST and RT), triangle RST satisfies the Pythagorean theorem, and therefore it is a right triangle.
In this case, the sides of triangle RST are ST = 5, RT = 12, and RS = 13. Let's calculate the square of the length of each side:
ST^2 = 5^2 = 25
RT^2 = 12^2 = 144
RS^2 = 13^2 = 169
Now, let's check if the Pythagorean theorem holds:
13^2 = 169
5^2 + 12^2 = 25 + 144 = 169
Since the square of the length of the hypotenuse (RS) is equal to the sum of the squares of the lengths of the other two sides (ST and RT), triangle RST satisfies the Pythagorean theorem, and therefore it is a right triangle.
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