Use the pythagorean theorem.
which we can quickly type as a^2+b^2=c^2. (The ^2 means squared.)
C is the hypotenuse, the longest length. It doesn't matter what you call a and b; just use the two shorter lengths.
So we're going to take each set of numbers, and if the square of the hypotenuse (c, the longest side) is equal to the sum of the squares of each length (the other two sides, a and b), then it's a right triangle. If it doesn't equal, then it's NOT a right triangle.
3,4,5:
3^2+4^2 = 9+16 = 25 = 5^2, so this IS a right triangle.
5, 12, 13:
5^2+12^2 = 25+144 = 169 = 13^2, so this IS a right triangle.
6,8,12:
6^2+8^2= 36+64 = 100. 12^2 = 144. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
6, 9, 12:
6^2+ 9^2 = 36+81 = 117. 12^2 = 144. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
8, 13, 26:
8^2 + 13^2 = 64+ 169 = 233. 26^2 = 676. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
8, 15, 17:
8^2+ 15^2 = 64 + 225 = 289. 17^2 = 289, so this IS a right triangle.
9, 12, 14:
9^2 + 12^2 = 81+144 = 225. 14^2 = 196. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
3, 8, 19:
3^2 + 8^2 = 9 + 64 = 73. 19^2 = 361. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.
0.5, 6, 3:
Oh, your teacher is trying to trick you bc the hypotenuse has been the last number with every other problem! 6 is the longest and that's your hypotenuse (c).
0.5^2 + 6^2 = 0.25 + 36 = 36.25. 6^2 = 36. These numbers do NOT work in the pythagorean theorem so this is NOT a right triangle.