Question

use the given information to prove that $\angle 8 \cong \angle 4$.
given: $r \parallel s$
prove: $\angle 8 \cong \angle 4$
step statement
1 $r \parallel s$
2 $\angle 8 \cong \angle 4$
select the rule
\\(\bigcirc\\) symmetric property
\\(\bigcirc\\) transitive property
\\(\bigcirc\\) addition and subtraction properties
\\(\bigcirc\\) multiplication and division properties
\\(\bigcirc\\) substitution property
\\(\bigcirc\\) definition of congruent angles
\\(\bigcirc\\) angle addition property

Explanation:

Step1: Identify given parallel lines

Given \(r \parallel s\)

Step2: Use transitive property via congruent angles

First, \(\angle 8 \cong \angle 2\) (vertical angles are congruent). Then \(\angle 2 \cong \angle 4\) (corresponding angles for parallel lines \(r \parallel s\)). By Transitive Property (if \(a \cong b\) and \(b \cong c\), then \(a \cong c\)), we get \(\angle 8 \cong \angle 4\).

Answer:

Transitive Property