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
Yes, because you can use the Pythagorean Theorem on any triangle
No, because the triangle is not a right triangle.
No, because the angle at point F is 90°.
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.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. To determine if the Pythagorean Theorem applies to this triangle, we need to check if it is a right triangle.
We know that the height EF is labeled 15 and the base DF is labeled 20. We also know that angle E measures 60 degrees and angle D measures 30 degrees. If the triangle is a right triangle, one of the angles must be 90 degrees.
Since the given angles are not 90 degrees, we can conclude that the triangle is not a right triangle. Therefore, the Pythagorean Theorem does not apply to this triangle.
So, the correct answer is:
No, because the triangle is not a right triangle.