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Chapter 2: Q16 (page 35)

Provide a counterexample to show that each statement is false.

Statement: If a four-sided figure has four congruent sides, then it has four right angles.

Short Answer

Expert verified

The given statement 鈥淚f a four-sided figure has four congruent sides, then it has four right angles.鈥� is false.

Step by step solution

01

Step 1. Define counterexample.

The counterexample is an example for which a hypothesis is true but the conclusion is false for an if-then statement.

02

Step 2. State the counterexample.

For a counterexample, draw a diagram with four equal sides such that it doesn鈥檛 form the right angles.

03

Step 3. State the conclusion.

The above figure has four congruent sides, but there are no four right angles. Thus, it is not necessary that a four-sided figure with four congruent sides has four right angles

Therefore, the above diagram is the counterexample, which shows that the statement is false.

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