The given triangles have side lengths of a, b, and c. Based on the values given in the table, which triangle is a right triangle? a b c triangle D triangle E triangle F triangle G A. triangle G B. triangle E C. triangle D D. triangle F
A triangle is a right triangle if it satisfies the Pythagorean theorem, which states that a² + b² = c², where c is the length of the hypotenuse (the side opposite the right angle).
Let's calculate the values of a² + b² for each triangle:
- For triangle D: 6² + 8² = 36 + 64 = 100
- For triangle E: 5² + 12² = 25 + 144 = 169
- For triangle F: 7² + 12² = 49 + 144 = 193
- For triangle G: 3² + 4² = 9 + 16 = 25
Based on the calculations above, the only triangle that satisfies the Pythagorean theorem and is a right triangle is triangle G. Therefore, the answer is A. triangle G.