Question

write the first step of an indirect proof for the given statement.
( mangle m = mangle n )
choose the correct answer below.
a. assume temporarily that ( mangle m ) and ( mangle n ) are not =.
b. assume temporarily that ( mangle m ) and ( mangle n ) are not always =.
c. assume temporarily that ( mangle m ) and ( mangle n ) are never =.
d. assume temporarily that sometimes ( mangle m = mangle n ).

Explanation:

Step1: Recall Indirect Proof

In an indirect proof (proof by contradiction), we start by assuming the negation of what we want to prove. Here, we want to prove \( m\angle M = m\angle N \), so the negation is that \( m\angle M \) and \( m\angle N \) are not equal.

Step2: Evaluate Options

• Option A: "Assume temporarily that \( m\angle M \) and \( m\angle N \) are not =" matches the negation needed for indirect proof.
• Option B: "not always =" is not the direct negation (the negation of "=" is "≠", not "not always =").
• Option C: "never =" is too strong (negation of "=" is "≠", not "never =").
• Option D: "sometimes \( m\angle M = m\angle N \)" is not the negation (we need to assume the opposite of \( m\angle M = m\angle N \)).

Answer:

A. Assume temporarily that \( m\angle M \) and \( m\angle N \) are not =