Does the Pythagorean Theorem apply to this triangle? How do you know?
(1 point)
O No, because the triangle is not a right triangle.
O No, because the angle at point F is 90"
O Yes, because you can use the Pythagorean Theorem on any triangle
O Yes, because it is a right triangle.
O No, because the triangle is not a right triangle.
The correct answer is:
O No, because the triangle is not a right triangle.
The Pythagorean Theorem applies only to right triangles, where one angle is a 90° angle. Since it is not mentioned that the triangle in question is a right triangle, we cannot use the Pythagorean Theorem to solve for its sides.
To determine if the Pythagorean Theorem applies to a triangle, we need to examine the angles of the triangle. According to the Pythagorean Theorem, it only applies to right triangles, which have one angle measuring exactly 90 degrees (denoted by a square box symbol) at one of the vertices.
Looking at the given answer choices, we see that two options mention a right triangle:
1. "No, because the triangle is not a right triangle" - This option states that the triangle is not a right triangle, which means the Pythagorean Theorem does not apply. This is a valid answer if the given triangle does not have a 90-degree angle.
2. "Yes, because it is a right triangle" - This option states that the triangle is a right triangle, which means the Pythagorean Theorem applies. If the given triangle indeed has a 90-degree angle, this would be the correct choice.
Therefore, to determine if the Pythagorean Theorem applies to the given triangle, we need to check if it is a right triangle. Since one of the answer choices states that "it is a right triangle," we can choose that option as the answer when we confirm that the triangle does have a 90-degree angle.