Fermat's triplets
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No, wrong mathematician. They are Pythagorean triplets.
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Yes, a right triangle has only one set of perpendicular lines.
The mode, I think is not always a number in the data set it represents, for example I have a set of numbers, 1,7,2,4,6. You'll put them in order; 1,2,4,6,7. And there is no number that is the mode. So, I believe that is correct.
No because the given sides do not comply with Pythagoras' theorem for a right angle triangle.
The two names of set squares are the right-angle triangle and the bevel. The right-angle triangle is commonly used in drafting and construction for creating and measuring right angles, while the bevel is used to measure angles other than 90 degrees.
A 90 degree angle and 2 acute angles will form a right angle triangle.