Does the Pythagorean Theorem apply to this triangle? How do you know?

Question

(1 point)
Responses

No, because the angle at point F
is 90°
.
No, because the angle at point cap f is 90 degrees .

No, because the triangle is not a right triangle.
No, because the triangle is not a right triangle.

Yes, because it is a right triangle.
Yes, because it is a right triangle.

Yes, because you can use the Pythagorean Theorem on any triangle
image given triangle
E 60 degrees
D 30 degrees
F not given
one side 15
another side 20

Answer 1

To determine whether the Pythagorean Theorem applies to a triangle, we need to check if the triangle is a right triangle (one angle is 90°).

In your case, you mentioned:

• Triangle E has an angle of 60 degrees
• Triangle D has an angle of 30 degrees
• Triangle F's angle is not given

Since the sum of the angles in any triangle must equal 180 degrees, we can find angle F:

• Angle E = 60°
• Angle D = 30°
• Angle F = 180° - (60° + 30°) = 90°

Since angle F is 90 degrees, triangle DEF is a right triangle.

The Pythagorean Theorem applies to right triangles, so the correct response is:

Yes, because it is a right triangle.