The Pythagorean Theorem is a well-known theorem that states that in any right triangle, the sum of the squares of the two sides is equal to the square of the hypotenuse. The converse of the theorem is also true, which states that if the sum of the squares of two sides of a triangle is equal to the square of the hypotenuse, then the triangle is a right triangle. This article will discuss the answer key to a homework assignment covering the Pythagorean Theorem and its converse.

## Using the Pythagorean Theorem to Solve Problems

The answer key to the first problem in the homework assignment is as follows: The length of the hypotenuse is 4, and the lengths of the other two sides are 3 and 4. This can be determined by using the Pythagorean Theorem. The theorem states that the sum of the squares of the two sides is equal to the square of the hypotenuse. In this case, the sum of the squares of the two sides is 3^2 + 4^2 = 9 + 16 = 25, and the square of the hypotenuse is 4^2 = 16. Since 25 = 16, this shows that the triangle is a right triangle and the lengths of the sides are 3, 4, and 4, respectively.

## Using the Converse of the Pythagorean Theorem to Solve Problems

The answer key to the second problem in the homework assignment is as follows: The triangle is not a right triangle. This can be determined by using the converse of the Pythagorean Theorem. The converse states that if the sum of the squares of two sides of a triangle is equal to the square of the hypotenuse, then the triangle is a right triangle. In this case, the sum of the squares of the two sides is 3^2 + 4^2 = 9 + 16 = 25, and the square of the hypotenuse is 5^2 = 25. Since 25 ≠ 25, this shows that the triangle is not a right triangle.

## Using Both the Pythagorean Theorem and Its Converse to Solve Problems

The answer key to the third problem in the homework assignment is as follows: The triangle is a right triangle. This can be determined by using both the Pythagorean Theorem and its converse. First, the sum of the squares of the two sides can be calculated by using the Pythagorean Theorem. The sum of the squares of the two sides is 3^2 + 4^2 = 9 + 16 = 25. Then, the converse can be used to determine if the triangle is a right triangle. Since the square of the hypotenuse is 25, this shows that the triangle is a right triangle.

The Pythagorean Theorem and its converse can be used to solve problems involving right triangles. This article has discussed the answer key to a homework assignment covering the Pythagorean Theorem and its converse. By using the Pythagorean Theorem and its converse, it is possible to determine if a triangle is a right triangle or not.