Which statement explains the Pythagorean Theorem?(1 point) Responses If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse. If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse. If all angles in a triangle are of equal measure, then the length of all sides will be equal. If all angles in a triangle are of equal measure, then the length of all sides will be equal. If a triangle is a right triangle, then the sum of the squares of the longest leg and the hypotenuse is equal to the square of the third side. If a triangle is a right triangle, then the sum of the squares of the longest leg and the hypotenuse is equal to the square of the third side. If the interior angles of a triangle add up to 180°, then the sum of the legs of the triangle is equal to the square of the hypotenuse.
If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
The correct statement explaining the Pythagorean Theorem is: "If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse."
The correct statement that explains the Pythagorean Theorem is: "If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse."
To understand and apply the Pythagorean Theorem, you need to know the following terms:
1. A right triangle is a triangle with one angle measuring 90 degrees.
2. The legs of a right triangle are the two sides that form the right angle.
3. The hypotenuse is the side opposite the right angle in a right triangle.
To use the Pythagorean Theorem, follow these steps:
1. Identify whether the given triangle is a right triangle.
2. Determine the lengths of the two legs.
3. Square the length of each leg.
4. Add the squares of the two leg lengths together.
5. Take the square root of the sum to find the length of the hypotenuse.
Applying the Pythagorean Theorem helps to establish the relationship between the lengths of the sides in a right triangle and is a fundamental concept in geometry and trigonometry.
Use the image to answer the question.
A triangle has the vertices labeled upper E upper F upper D. The height upper E upper F is labeled 15, the base upper D upper F is labeled 20, and the hypotenuse upper D upper E is labeled 25. Angle upper E measures 60 degrees and angle upper D measures 30 degrees.
Does the Pythagorean Theorem apply to this triangle? How do you know?
(1 point)
Responses
No, because the angle at point F is 90°.
No, because the angle at point cap f is 90 degrees .
Yes, because it is a right triangle.
Yes, because it is a right triangle.
No, because the triangle is not a right triangle.
No, because the triangle is not a right triangle.
Yes, because you can use the Pythagorean Theorem on any triangle
Yes, because you can use the Pythagorean Theorem on any triangle