A right triangle is a triangle with one angle measuring 90 degrees, also known as a right angle. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares o...
Pythagorean Theorem
The Pythagorean theorem is a fundamental principle in geometry that relates the sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs). Mathematically, it can be expressed as:
a² + b² = c²
Where:
- a and b are the lengths of the legs
- c is the length of the hypotenuse
Applying the Pythagorean Theorem
To determine if triangle AWXY is a right triangle, we need to check if the lengths of its sides satisfy the Pythagorean theorem. We are given the following side lengths:
- AW = 34√17
- WX = √17
- AY = √17
Let's assume that AW is the hypotenuse, as it's the longest side. Applying the Pythagorean theorem:
(34√17)² = (√17)² + (√17)²
Simplifying the equation:
1156 * 17 = 17 + 17
19652 = 34
The equation is not true, indicating that the lengths of the sides do not satisfy the Pythagorean theorem. Therefore, triangle AWXY is not a right triangle.
Conclusion
Based on the given side lengths, we can conclude that triangle AWXY is **not** a right triangle. The sides do not satisfy the Pythagorean theorem, indicating that the triangle does not have a right angle.