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Chapter 6: Q2. (page 215)

What is the first sentence of an indirect proof of the statement shown?

ΔABC is equilateral.

Short Answer

Expert verified

The first sentence of an indirect proof of the statement “ΔABCis equilateral” is“Assume that ΔABCis not equilateral.”.

Step by step solution

01

Step 1. Define concept of indirect proof of the statement

An indirect proof is a proof wherein you begin by assuming temporarily that the desired conclusion is not true which then by reasoning logically reaches to a certain contradiction or some other known fact.

02

Step 2. Steps of writing an indirect proof

1. Assume temporarily that the conclusion is not true.

2. Reason logically until you reach a contradiction.

3. Point out that the assumption was wrong and the conclusion must then be true.

03

Step 3. State the first sentence of indirect proof of the statement

Consider the following statement:ΔABCis equilateral.

In order to write out the first sentence of an indirect proof of this statement, state the temporary assumption that the given conclusion is not true.

Therefore, in this case, the first sentence to be used to write this proof is: “Assume that ΔABCis not equilateral.”

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