Which statement explains the Pythagorean Theorem?(1 point)
Responses
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 legs is equal to the square of the hypotenuse.
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 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."
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 how to get to this answer, let's break down the Pythagorean Theorem. The Pythagorean Theorem is a fundamental concept in geometry that relates to right triangles, which are triangles with one angle measuring 90 degrees (a right angle).
The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, known as the legs.
To understand why this is true, you can use a visual proof or algebraic proof.
One way to visualize the Pythagorean Theorem is by using squares. If you draw a right triangle and construct squares on each side, the areas of these squares will follow a specific relationship. The square on the hypotenuse will have an area equal to the sum of the areas of the squares on the legs.
An algebraic way to prove the Pythagorean Theorem is by assigning variables to the lengths of the sides of the triangle. Let's call the lengths of the legs "a" and "b" and the length of the hypotenuse "c". Using the Pythagorean Theorem, we have the equation a^2 + b^2 = c^2.
So, in summary, the statement that correctly explains the Pythagorean Theorem is that if a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse.