Statement: If a triangle is a right triangle , then the square of the longest side of the triangle is equal to the sum of the squares of the other two sides. What is the INVERSE of the statement? The square of the longest side of the triangle is equal to the sum of the squares of the other two sides if and only if the triangle is a right triangle. If the square of the longest side of the triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. If a triangle is not a right triangle.,then the square of the longest side of the triangle is not equal to the sum of the square of the other two sides. If the square of the longest side of the triangle is not equal to the sum of the squares of the other two sides , then the triangle is not a right triangle.

## Step 1<br />The problem involves understanding the concept of inverse statements in logic. An inverse statement is formed by negating both the hypothesis and the conclusion of a conditional statement.<br /><br />## Step 2<br />The original statement is: "If a triangle is a right triangle, then the square of the longest side of the triangle is equal to the sum of the squares of the other two sides."<br /><br />## Step 3<br />To form the inverse of this statement, we need to negate both the hypothesis and the conclusion. The hypothesis is "a triangle is a right triangle" and the conclusion is "the square of the longest side of the triangle is equal to the sum of the squares of the other two sides."<br /><br />## Step 4<br />Negating the hypothesis, we get "a triangle is not a right triangle." Negating the conclusion, we get "the square of the longest side of the triangle is not equal to the sum of the squares of the other two sides."<br /><br />## Step 5<br />Combining these negated parts, we get the inverse statement: "If a triangle is not a right triangle, then the square of the longest side of the triangle is not equal to the sum of the squares of the other two sides."