Question

Example 4 Find a counterexample for each conditional statement.

If the four sides of a quadrilateral are congruent, then the shape is a square.

Short answer

The statement that "if the four sides of a quadrilateral are congruent, then the shape is a square is not always true."

Step-by-step solution

Step 1. Given Statement.

If the four sides of a quadrilateral are congruent, then the shape is a square.

Step 2. Description of step.

To find a counterexample for the given statement.

It is given that four sides of a quadrilateral are congruent.

Since the four sides of a square are also congruent, hence the quadrilateral can be a square.

But the four sides of a rhombus are also congruent, then the quadrilateral may be rhombus also.

Step 3. Conclusion.

Therefore, the statement that "four sides of a quadrilateral are congruent, then the shape is a square is not always true."