The question is asking which statement correctly defines the Pythagorean Theorem.

The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (called the legs). Mathematically, it's expressed as:

$a^2 + b^2 = c^2$ where:

• $a$ and $b$ are the lengths of the legs, and
• $c$ is the length of the hypotenuse.

Now, let’s analyze the choices:

• A: Describes an obtuse triangle, not the Pythagorean Theorem.
• B: Describes a right triangle but incorrectly claims that the sum of the squares of the legs is less than the square of the hypotenuse.
• C: Describes an obtuse triangle, which does not follow the Pythagorean Theorem.
• D: Correctly describes the Pythagorean Theorem.

Thus, the correct answer is D: "In a right triangle, the sum of the squares of the leg lengths is equal to the square of the hypotenuse length."

Would you like further clarification on this, or do you have any other questions?

Here are five questions to explore the concept further:

1. How is the Pythagorean Theorem used to determine the distance between two points in a coordinate plane?
2. Can the Pythagorean Theorem be applied to non-right triangles? Why or why not?
3. What are some real-world applications of the Pythagorean Theorem?
4. How do you derive the converse of the Pythagorean Theorem?
5. What are the implications of the Pythagorean Theorem in three-dimensional geometry?

Tip: The Pythagorean Theorem only applies to right triangles, so always check the angle before applying the formula.