Chapter SR28, Problem 4P

Solution

Rewrite the conditional statement in if-then form. Then write its converse and tell whether the converse is true or false.

True.

Given:

In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

Concept used:

• A conditional statement has two parts, a hypothesis and a conclusion. When a conditional statement is written in if-then form, the “if” parts contains the hypothesis and the “then” part contains the conclusion.
• The converse of a conditional statement is formed by switching the hypothesis and the conclusion.

Calculation:

Given - In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

If-then form: If the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse then it is a right triangle.

Converse: If it is a right triangle then the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse

True.