Which statement explains the Pythagorean Theorem?
1. 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
2. If all angels in the a triangle are of equal measure, Then the length of all sides will be equal
3. 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
4. If a triangle is a right triangle, then the sum of the squares of the legs is equal to the square of the hypotenuse
4. 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:
4. 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 option 4: "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 and prove the Pythagorean Theorem, you can use the following steps:
1. Start with a right triangle, which is a triangle that contains one angle measuring 90° (also known as a right angle).
2. Label the lengths of the three sides of the triangle. The two shorter sides are called the legs, and the longest side is called the hypotenuse.
3. Assign variables to the lengths of the legs (a and b) and to the length of the hypotenuse (c). This will allow us to generalize the theorem.
4. Express the relationship between the sides of the triangle using the formula: a^2 + b^2 = c^2. This equation is the Pythagorean Theorem.
5. Verify the Pythagorean Theorem by squaring the lengths of the legs and adding them together. Then, square the length of the hypotenuse and compare the two values. If they are equal, the theorem holds true.
It's important to note that the Pythagorean Theorem only applies to right triangles. It provides a relationship between the lengths of the sides and allows us to calculate the length of any missing side when the lengths of the other sides are known.