Chapter 6.3, Problem 9ST1

To determine

To write: a correct first sentence of the indirect proof.

Answer to Problem 9ST1

Assume that $AC\ne 14$ .

Explanation of Solution

Given information:

If $\Delta ABC$ is acute, then $m\angle C\ne 90°$

Given:

Suppose plan to write an indirect proof of the statement: If $AB=7$ , then $AC=14$ .

Calculation:

Consider the statement:

If $AB=7$ , then $AC=14$

An indirect proof is to be written.

Write a correct first sentence for this proof.

Start off an indirect proof by assuming temporarily that the given conclusion is not true.

Hence, in this case, the first sentence to be used to write this proof is:

Assume that $AC\ne 14$ .