Which statement explains the Pythagorean theorem? 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 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 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 lengths of the two legs is equal to the square of the length 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 lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse)."
The statement that explains the Pythagorean theorem is: "If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse."
To understand the Pythagorean theorem, let's break it down step by step:
1. Start with a right triangle: A right triangle is a triangle that has one angle measuring 90 degrees (a right angle).
2. Identify the legs and the hypotenuse: In a right triangle, the two sides that form the right angle are called the legs, while the side opposite the right angle is called the hypotenuse.
3. Square the lengths of the legs: Take the lengths of the legs, and multiply each length by itself (raise it to the power of 2). This gives you the squares of the legs.
4. Square the length of the hypotenuse: Take the length of the hypotenuse, and also multiply it by itself (raise it to the power of 2). This gives you the square of the hypotenuse.
5. Compare the sums: The Pythagorean theorem states that the sum of the squares of the legs is equal to the square of the hypotenuse. In other words, if you add up the squared lengths of the legs, it will be equal to the squared length of the hypotenuse.
So, in mathematical terms, the Pythagorean theorem can be written as: a^2 + b^2 = c^2, where 'a' and 'b' represent the lengths of the legs, and 'c' represents the length of the hypotenuse in a right triangle.