Final answer:
The triangles that do not form right triangles are Triangles C (10, 12, 15), D (3, 6, ∙ 45), and E (7, 8, 113), as their sides do not satisfy the Pythagorean theorem.
Step-by-step explanation:
To determine which triangles do not form right triangles, we will apply the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). If a triangle's side lengths do not fulfill the equation a² + b² = c², then it is not a right triangle.
Let's check each triangle:
- Triangle A: 3² + 4² = 9 + 16 = 25 which equals 5², so it forms a right triangle.
- Triangle B: 5² + 12² = 25 + 144 = 169 which equals 13², so it forms a right triangle.
- Triangle C: 10² + 12² = 100 + 144 = 244 which is not equal to 15² (225), so it does not form a right triangle.
- Triangle D: 3² + 6² = 9 + 36 = 45 which should equal (∙ 45) but the correct value is √45 which equals 6.71 (approx.), so it does not form a right triangle.
- Triangle E: 7² + 8² = 49 + 64 = 113 which does not equal 113², so it definitely does not form a right triangle.
Therefore, the triangles that do NOT form right triangles are Triangles C, D, and E.