Question

complete the proof that \\( \angle sru \cong \angle rut \\).

1 ( \overleftrightarrow { tv } \parallel \overleftrightarrow { qs } ) given
2 ( \angle rut \cong \angle prq )
3 ( \angle prq \cong \angle sru )
4 ( \angle sru \cong \angle rut )

Explanation:

Step1: Identify vertical angles

$\angle RUT$ and $\angle PRQ$ are vertical angles, so they are congruent.

Step2: Use transitive property

Given $\angle PRQ \cong \angle SRU$ and $\angle RUT \cong \angle PRQ$, substitute to get $\angle SRU \cong \angle RUT$.

Answer:

The reason for step 4 is Substitution.