We have a statement that shows the congruent segments as follows.

\overline{A B} ≅ \overline{C D}

Now we will state an assumption that we would make to start an indirect proof. Before stating the assumption, recall that an indirect proof starts with the assumption that the statement we are trying to prove is not true. In this case, the statement is that

\overline{A B}

is congruent to

\overline{C D} .

The negation of this statement is that the two segments are not congruent.

\overline{A B} is congruent to \overline{C D} . ⇓ \overline{A B} is not congruent to \overline{C D} .

Finally, we can state the assumption we would make to start the indirect proof.

Assumption : \overline{A B} ≆ \overline{C D}

Extra

Indirect Proof

Indirect reasoning is used when we make an assumption that a conclusion of a statement is false and show that this assumption led to a contradiction. Moreover, indirect proof, or proof by contradiction, is used in indirect reasoning as a proof method. An indirect proof can be written in three steps.

Identify the statement to be proven and temporarily assume that its negation is true.
Use logical reasoning until a contradiction is derived.
State that the original statement must be true because the contradiction shows that the assumption is false.

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Indirect Proof

Exercise