Which statement explains the Pythagorean Theorem?(1 point)
Responses
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 all angles in a triangle are of equal measure, then the length of all sides will be equal.
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.
If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.
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.
Yes, because you can use the Pythagorean Theorem on any triangle
Yes, because you can use the Pythagorean Theorem on any triangle
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.
The 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 why this statement explains the Pythagorean Theorem, we need to understand the components involved. The Pythagorean Theorem is a mathematical concept that applies specifically to right triangles – triangles with one angle measuring 90 degrees.
In any right triangle, there are three sides – two legs and one hypotenuse. The legs are the two sides that form the right angle, while the hypotenuse is the side opposite the right angle.
The Pythagorean Theorem states that the sum of the squares of the lengths of the legs (the shorter sides) is equal to the square of the length of the hypotenuse (the longest side).
To find the length of a side using the Pythagorean Theorem, you can follow these steps:
1. Identify the two legs of the right triangle.
2. Label them as 'a' and 'b' (or any other variables you prefer).
3. Square each leg, which means multiplying each leg by itself.
4. Add the squares of the legs together.
5. Take the square root of the sum to find the length of the hypotenuse.
For example, let's say we have a right triangle with one leg measuring 3 units and the other leg measuring 4 units. To find the length of the hypotenuse, we can use the Pythagorean Theorem:
a = 3
b = 4
a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25
Taking the square root of 25 gives us the length of the hypotenuse:
√25 = 5
Therefore, the length of the hypotenuse in this triangle is 5 units. This calculation illustrates how the Pythagorean Theorem can be applied.
So, in summary, the Pythagorean Theorem explains that in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse.