Question

$overleftrightarrow{tu} perp overleftrightarrow{st}$ and $overleftrightarrow{pq} perp overleftrightarrow{qr}$. complete the proof that $angle stu cong angle pqr$.

statement	reason
2. $overleftrightarrow{pq} perp overleftrightarrow{qr}$	given
3. $mangle stu = 90^circ$	definition of perpendicular lines
4. $mangle pqr = 90^circ$	definition of perpendicular lines
5. $mangle stu = mangle pqr$	transitive property of equality
6. blank	blank

Explanation:

Step1: Recall congruence of angles

If two angles have equal measures, then they are congruent.
We know from step 5 that \( m\angle STU = m\angle PQR \).

Step2: Apply the definition of congruent angles

By the definition of congruent angles (if \( m\angle A=m\angle B \), then \( \angle A\cong\angle B \)), we can conclude that \( \angle STU\cong\angle PQR \).

Answer:

\( \angle STU \cong \angle PQR \) (Reason: Definition of congruent angles (or Angles with equal measures are congruent))