FTCE General Knowledge Math Practice Test

What theorem relates the lengths of the sides of a right triangle?

1. Triangle inequality theorem

2. Pythagorean theorem

3. Concurrent theorem

4. Sine theorem

The correct answer is: Pythagorean theorem

The Pythagorean theorem addresses the relationship between the lengths of the sides of a right triangle. It 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. This can be expressed mathematically as \(c^2 = a^2 + b^2\), where \(c\) represents the hypotenuse and \(a\) and \(b\) are the other two sides. This theorem is fundamental in geometry and establishes a clear and quantifiable relationship between the sides of right triangles, which is critical for solving various mathematical problems related to triangles. In contrast, the triangle inequality theorem deals with the relationships between the lengths of the sides of any triangle, stating that the sum of the lengths of any two sides must be greater than the length of the remaining side. The concurrent theorem pertains to lines and angles, rather than the side lengths of triangles. The sine theorem, also known as the law of sines, is relevant for non-right triangles and describes the relationship between the lengths of sides and the sines of their opposite angles.