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Chapter 2: Q15 (page 35)

Provide a counterexample to show that each statement is false.

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

Short Answer

Expert verified

The given statement 鈥淚f a four-sided figure has four right angles, then it has four congruent sides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 the diagram if four unequal sides such that it has four right angles.

03

Step 3. State the conclusion.

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

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

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Most popular questions from this chapter

Copy everything shown and write a two-column proof.

Given:m鈭�1=m鈭�2;

m鈭�3=m鈭�4;

Prove:m鈭�SRT=m鈭�STR

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.

What can you conclude if the following sentences are all true?

  1. If(1) p, then q.
  2. (2) p
  3. I(3) q, then not r.

(4) s or r

State the hypothesis and the conclusion of each conditional.

if

State the number that is paired with the bisector of 鈭�CDE.
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