To translate the mathematical statement "If two sides of a triangle are equal in length [tex]$(p)$[/tex], the angles opposite those sides are congruent [tex]$(q)$[/tex]" into symbolic form, we need to identify the correct type of logical statement.
The given statement is a conditional statement. A conditional statement is typically formulated in the form "If [tex]$p$[/tex], then [tex]$q$[/tex]" which is symbolically represented as [tex]\( p \rightarrow q \)[/tex].
Here are the steps for translating the statement:
1. Identify the Hypothesis (Antecedent):
The hypothesis in this statement is "two sides of a triangle are equal in length," which we can denote as [tex]\( p \)[/tex].
2. Identify the Conclusion (Consequent):
The conclusion is "the angles opposite those sides are congruent," which we can denote as [tex]\( q \)[/tex].
3. Formulate the Conditional Statement:
The logical structure of "If [tex]\( p \)[/tex], then [tex]\( q \)[/tex]" is represented symbolically as [tex]\( p \rightarrow q \)[/tex].
Thus, the correct symbolic form is:
[tex]\[ p \rightarrow q \][/tex]
Therefore, the answer to the question is:
[tex]\[
p \rightarrow q
\][/tex]
